Algebra and Trigonometry (5th Edition)

Chapter 2

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Domain:Range: ; Determine the domain of the ... more

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Domain:Range: ; Determine the domain of the ... more

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Domain:Range: ; Determine the domain of the ... more

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Domain:Range: ; Determine the domain of the ... more

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Domain:Range: ; The domain of the given function ... more

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Domain:Range: ; The domain of the given function ... more

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Relative maximum: at Increasing: Decreasing: ; ... more

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Relative minimum: 2 at Increasing: Decreasing: ; ... more

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Relative maximum: at Relative minimum: 0 at ... more

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Relative maximum: at Relative minimum: at ... more

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Increasing:; Decreasing:The relative minimum of ... more

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Increasing: ; decreasing: The relative maximum of ... more

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Increasing: ; decreasing: The relative maximum of ... more

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Increasing:; decreasing:The relative minimum of ... more

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Increasing: ; decreasing: The relative minimum of ... more

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Increasing: ; decreasing: The relative maximum of ... more

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; Let and represent the length and width, ... more

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; Let represent the height of the triangular ... more

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; Draw aright-angled triangle . ; Use the ... more

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; Let the object B reach a point in time . ... more

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; Let and be the width and length of the ... more

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; Let and represent the length and width, ... more

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; Represent the given situation with the help of ... more

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; The tank is the combination of two hemispheres ... more

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; ; ; ; As is less than or equal to 1, use the ... more

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; ; ; ; As is less than or equal to , use the ... more

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; ; ; ; As is greater than or equal to and less ... more

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; ; ; ; As is less than to , use the formula to ... more

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Substitute values less than 0 for into function ... more

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Substitute different values of from the interval... more

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Substitute different values of from the interval... more

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Substitute different values of from the interval... more

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Plot the graph of for the inputs , which are less... more

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Plot the graph of for the inputs , which are less... more

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Plot the graph for the inputs , which are less ... more

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The denominator of the expression is nonzero for.... more

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The denominator of the expression is nonzero for... more

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The denominator of the expression is nonzero for... more

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The greatest integer function gives each output as... more

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The greatest integer function gives each output as... more

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The greatest integer function gives each output as... more

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The greatest integer function gives each output as... more

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Domain:; range: ; It can be observed from the ... more

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Domain:; range: ;  It can be observed from the ... more

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Domain:; range: ;  It can be observed from the ... more

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Domain:; range: ;  It can be observed from the ... more

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Domain:; range: ; It can be observed from the ... more

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Domain:; range: ; It can be observed from the ... more

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Domain: ; Range: ; The domain of the given ... more

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Domain: ; Range: ; The domain of the given ... more

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Domain:; Range: ; The domain of the given function... more

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Domain: ; Range: ; The domain of the given ... more

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Domain:; Range:; ;  It can be observed from the ... more

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Domain:;Range:; ; It can be observed from the ... more

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; Simplify the given equation. ; Write the value ... more

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; ; Add to both sides of given equation. ; ... more

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; implies that the output for the greatest ... more

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; Apply the root on both sides of the equation... more

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33 ; The domain of both the given functions is the... more

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; The domain of both the given functions is the ... more

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; The domain of both the given functions is the ... more

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5 ; The domain of both the given functions is the ... more

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Does not exist ; The domain of both the functions ... more

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; The domain of both the given functions is the ... more

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0 ; The domain of both the given functions is the ... more

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0 ; Substitute for into the function and solve ... more

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1 ; The domain of both the given functions is the ... more

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; Substitute the respective values of function ... more

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Does not exist ; The domain of the function is ... more

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; The domain of the function is the set of real ... more

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; Substitute the respective values of function ... more

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Does not exist ; Substitute the respective values ... more

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; The domain of the function is the set of real ... more

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; The domain of the function is the set of real ... more

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Domain of : Domain of : Domain of : ; The graph of... more

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Domain of : Domain of : Domain of : ; The domain ... more

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; The domain of is and the domain of is .The ... more

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The graph of the function lies between the ... more

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The graph of the function lies between the ... more

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The graph of the function lies between the ... more

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  Domain of:  Domain of: Domain of: ;  The graph ... more

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Domain of : Domain of : Domain of : ;  The domain ... more

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; The domain of is and the domain of is .The ... more

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Make a table by using the given graph information ... more

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Substitute the values of functions  and  at ... more

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Substitute the values of functions  and  at ... more

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3 ; Evaluate by replacing with in . ; Substitute... more

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4 ; Evaluate by replacing with in . ; ... more

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6 ; Evaluate by replacing with in . ; ... more

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5 ; Evaluate by replacing by into . ; ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function, . ; ... more

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; Substitute for into the given function, . ; ... more

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; Substitute for into . ; Use identity to ... more

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; Substitute for into the given function . ; ... more

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; Substitute for into the given function . ; ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function . ; ... more

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; Substitute for into the given function . ; ... more

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; Substitute for into the given function . ; ... more

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; Substitute for into the given function to ... more

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Substitute 0 for into the given equation and ... more

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Substitute 0 for into the given equation and ... more

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Substitute 0 for into the given equation and ... more

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Substitute arbitrary values of and solve to find ... more

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; ; The domain of is equal to the intersection of... more

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Domain of:; Domain of:; Domain of:; Domain of: ; ... more

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; Equate the denominator of to 0 to find the ... more

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; Substitute for into the equation, . ; ... more

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29 ; Substitute for into the equation, . ; ... more

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64 ; Substitute 1 for into the equation, . ; ... more

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; Substitute 1 for into the equation, . ; ... more

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218 ; Substitute 5 for into the equation, . ; ... more

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; Substitute for into the equation, . ; ... more

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; Substitute for into the equation, . ; ... more

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; Substitute 3 for into the equation, . ; ... more

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; Calculate first, to find.Substitute for into... more

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9 ; Calculate first, to find .Substitute 3 for ... more

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512 ; Calculate first, to find.Substitute 2 for ... more

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; Calculate first, to find.Substitute for into... more

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; Calculate to find .Substitute for into the ... more

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13 ; Calculate to find.Substitute 1 for into the... more

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; Calculate to find .Substitute into the given ... more

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; Calculate to find.Substitute into the given ... more

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;Domain of : Domain of : ; Substitute for into ... more

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;Domain of : Domain of : ; Substitute for into ... more

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; Domain of : and : ; Substitute the given value ... more

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; Domain of : and  : ; Substitute the given value ... more

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; Domain of : and : ; Substitute the given value ... more

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; Domain of : and : ; Substitute the given value ... more

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 ; Domain of is and is ; Substitute the given ... more

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 ; Domain of is and is ; Substitute the given ... more

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; Domain of : and : ; Substitute the given value ... more

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; Domain of : and : ; Substitute the given value ... more

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; Domain of :; Domain of : ; To evaluate , ... more

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; Domain of:; Domain of: ; To evaluate , ... more

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; Domain of is and is .  ; Substitute the given ... more

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; Domain of :; Domain of : ; To evaluate , ... more

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; Domain of : ; Domain of : ; To evaluate , ... more

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; Domain of :; Domain of : ; To evaluate , ... more

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; Domain of :; Domain of : ; To evaluate , ... more

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; Domain of : ; Domain of : ; To evaluate , ... more

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 ; Domain of is and is .  ; Substitute the given... more

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; Domain of : ; Domain of : ; To evaluate , ... more

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; Domain of is and is .  ; Substitute the given ... more

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 ; Domain of is and is . ; Substitute the given ... more

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; is the function whose power is raised to 5.... more

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; is the function whose power is raised to .... more

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; is the function whose power is raised to 4.... more

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; is the function whose power is raised to .... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; ; Write the two functions, and , that can be ... more

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; The function that gives the size in country A ... more

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; The new cost price is dollars.Find the selling... more

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Compare the equation with the slope-intercept ... more

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 Compare the equation with the general form of ... more

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 Compare the equation with the slope-intercept ... more

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Compare the equation with the slope-intercept ... more

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 Substitute 0 for into the given equation.Since ... more

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 Compare the equation with the slope-intercept ... more

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Compare the equation with the slope-intercept ... more

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Compare the equation with the slope-intercept ... more

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The composition makes sense, while is not ... more

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:;: ; Write two functions and such that both ... more

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A point on the graph of a function is the point ... more

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Assume two functions f and g. The functions , , ... more

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The function is not equal to the function for ... more

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Relative maximum: at Relative minimum: ... more

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Domain:; Range: ; The domain of a function is the ... more

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; According to the given conditions, the window ... more

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;;; ; Identify the part of the domain which ... more

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Graph for the inputs that are less than; this ... more

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1 ; Substitute the respective values of and into... more

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; Substitute the respective values of and into... more

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5 ; Substitute the respective values of and into... more

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Does not exist ; Substitute the respective values ... more

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4 ; Substitute for in to evaluate . ; ... more

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; Substitute for in to evaluate . ; Use the ... more

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6 ; Substitute the value of the function into the... more

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28 ; Substitute the value of the function into ... more

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; Substitute the value of the function into the ... more

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102 ; Substitute the value of the function into ... more

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Domain of : Domain of :Domain of :Domain of : ; ... more

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Domain of : Domain of :Domain of :Domain of : ; ... more

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The graph of will be units below the graph of... more

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If is equal to 0 at any point, then the domains ... more

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For two linear functions and , the domain of ... more

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The domain of is not only restricted to those ... more

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-axis: No; -axis: Yes; Origin: No ; When the given... more

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-axis: No; -axis: Yes; Origin: No  ; When the ... more

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-axis: Yes; -axis: No; Origin: No  ; When the ... more

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The graph is not symmetric about the axis or the ... more

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The graph is not symmetric about the axis or the ... more

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The graph is symmetric about the axis, the axis, ... more

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The graph is not symmetric about the axis and the ... more

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The graph is not symmetric about the -axis, axis, ... more

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-axis: No-axis: NoOrigin : No ; Draw the graph of ... more

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-axis: No-axis: NoOrigin : No ; Draw the graph of ... more

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-axis: No-axis: YesOrigin : No ; Draw the graph of... more

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-axis: No-axis: YesOrigin : No ; Draw the graph of... more

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The graph is not symmetric with respect to -axis ... more

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The graph is not symmetric with respect to -axis ... more

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The graph is symmetric with respect to the origin... more

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The graph is symmetric with respect to the origin... more

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The graph is symmetric with respect to the -axis, ... more

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The graph is not symmetric with respect to any of ... more

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The graph is not symmetric with respect to the x-... more

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The graph is not symmetric with respect to the x-... more

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The graph is symmetric with respect to the x-axis... more

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The graph is symmetric with respect to the x-axis... more

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-axis: no; -axis: no; origin: no ; Replace y by ... more

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-axis: yes; -axis: no; origin: no ; Replace y by ... more

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The graph is not symmetric with respect to the x-... more

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The graph is not symmetric with respect to the x-... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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axis: ; axis: ; Origin: ; For any point to be ... more

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In the graph given in problem 33, check the ... more

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For the function given in problem 41, replacewith ... more

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Substitute different values of from the interval... more

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From the university of CB : 3576; From the ... more

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The graph is not symmetric with respect to the y-... more

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The graph is not symmetric with respect to the x-... more

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Replaceby . ; Replace byin the given function... more

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Replaceby . ; Replace by in the given function... more

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Let where and be two odd functions such that and.... more

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Let where and be two even functions such that ... more

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Let where is an even function such that and is ... more

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 The graph of is stretched vertically if and ... more

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The graph of the given function can be obtained ... more

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The graph of the given function can be obtained ... more

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The graph of the given function can be obtained ... more

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The graph of the given function can be obtained ... more

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Reflect the graph of the function across the -... more

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Shift the graph of to the right by 1 unit. ; The ... more

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Shift the graph of upward by 4 units. ; The graph... more

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Shift the graph of to the right by 2 units. ; The... more

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Multiply the -coordinate by 3 units to stretch the... more

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Multiply the coordinate by 2 units to stretch the ... more

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Multiply the coordinate by units to shrink the ... more

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Reflect the graph of the function about the -axis... more

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Shift the graph of the function to the right by 2... more

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Shift the graph of the function to the left by 1 ... more

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Shift the graph of the function to the left by 1 ... more

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Reflect the graph of the function about the -axis... more

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Multiply the coordinate by units to shrink the ... more

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Reflect the graph of the function about the -axis... more

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Shift the graph of the function towards left by 2 ... more

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Shift the graph of the function towards right by ... more

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Shift the graph of the function down by 2 units... more

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Shift the graph of the function, towards left by ... more

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Divide -coordinate of each of the points that lie ... more

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Multiply -coordinate for each of the points that ... more

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Multiply -coordinate of each of the points that ... more

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Shift the graph of the function towards right by ... more

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Multiply the coordinates by 3 units to stretch the... more

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Reflect the graph of across the -axis and then ... more

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Multiply the -coordinate of each of the point on ... more

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Multiply the y-coordinate of each of the points ... more

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Shift the graph of the function to the right by 5... more

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Reflect the graph of the basic function across ... more

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Shift the graph of the function to the left by 3 ... more

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Reflect the graph of the function about y-axis ... more

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Shift the graph of the function to the right by 3... more

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Shift the graph function to the left by 4 units ... more

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; The graph of function can be found by vertical... more

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; The graph of function can be obtained by ... more

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; The graph of function can be obtained by ... more

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; The graph of the function can be obtained from... more

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; The graph of function can be obtained from the... more

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; The graph of can be obtained by horizontally ... more

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; The graph of can be obtained from the graph of... more

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; The graph of is the reflection of the graph of... more

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Assume the function . The function is obtained by... more

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; The graph of is the graph of shifted right by... more

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; When the graph of is shifted to the left by ... more

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; When the graph of is shifted to the left by ... more

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; When the graph of is shifted to the right by ... more

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         ; When the graph of is shrunken or ... more

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                 ; When the graph of is shifted ... more

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; When the graph of is shifted to the right by ... more

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; When the graph of is shrunken or stretched ... more

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; When the graph of is reflected across the axis... more

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; When the graph of is reflected across the axis... more

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The absolute value of is greater than 1, so ... more

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The absolute value of is less than 1, so ... more

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Stretch the given graph vertically by a factor of... more

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Horizontally shrink the given graph of by a factor... more

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Shift the given graph by 1 unit to the right to ... more

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Shift the given graph by 1 unit to the left along ... more

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The required graph is of the form , which can be ... more

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The required graph is of the form , which can be ... more

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The graph of is the graph of shifted by 2 units ... more

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The graph of is obtained by reflecting the graph ... more

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Since , the graph of is a horizontal shrinking of ... more

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The graph of is the graph of shifted by 1 unit ... more

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The graph of is obtained by reflecting the graph ... more

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Step : 1 Substitute for x into the given function... more

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No ; Substitute for x into the given function... more

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; Add 2 to the -coordinate of the points , , , ... more

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; Multiply the -coordinate of the points , , , ... more

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; Subtract 1 from the -coordinate of the points... more

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; Add 2 to the -coordinates and 1 to the -... more

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-axis : No-axis : YesOrigin : No ; Replace by in... more

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-axis: Yes- axis: NoOrigin: No ; Replace by in ... more

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-axis: no-axis: noOrigin: yes ; Replace by in ... more

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40,504 ; Familiarize: Let be the number of item P... more

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1,123 ; Familiarize: Let be the number of item G ... more

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29,725 acres ;  Familiarize: Let be the total ... more

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Determine the coordinates of the transformed graph... more

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Determine the coordinates of the transformed graph... more

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Determine the coordinates of transformed graph by... more

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Determine the coordinates of transformed graph by... more

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; The given graph of is the shifted graph of the... more

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The coordinate's shows that the graph of is ... more

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Variation constant:Equation of variation: ; The ... more

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Variation constant:Equation of variation: ; The ... more

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Variation constant: 36Equation of variation: ; The... more

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Variation constant: 60Equation of variation: ; The... more

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Variation constant:4Equation of variation: ; The ... more

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Variation constant: Equation of variation: ; The ... more

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Variation constant: 4Equation of variation: ; The ... more

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Variation constant: Equation of variation: ; The ... more

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Variation constant:  Equation of variation: ; The ... more

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Variation constant: 7Equation of variation: ; The ... more

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 Variation constant:  Equation of variation: ; The... more

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Variation constant: Equation of variation: ; The ... more

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; Let the weekly allowance be and the child's ... more

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; Let the sales tax paid on product be and the ... more

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hour ; The equation for the given variation ... more

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686 kg ; The equation for the given variation ... more

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90 g ; Let the fat in a diet be and the weight be... more

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36 ; The equation for the given variation ... more

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hr ; The equation for the given variation ... more

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27 min ; The equation for the given variation ... more

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cm ; The equation for the given variation ... more

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; The equation for the given variation condition ... more

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feet  ; The equation for the given variation ... more

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lb ; The equation for the given variation ... more

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; Substitute 2 for into the equation as the ... more

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; Substitute 2 for into the equation as the ... more

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; The equation for the given variation condition ... more

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. ; The equation for the given variation condition... more

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; The equation for the given variation condition ... more

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; The equation for the given variation condition ... more

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; The equation for the given variation condition ... more

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; The equation for the given variation condition ... more

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; The equation for the given variation condition ... more

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; The equation for the given variation condition ... more

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meter ; The equation for the given variation ... more

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mph ; Let the atmospheric drag be . So, the ... more

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36 mph ; The equation for the given variation ... more

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  ; The equation for the given variation condition... more

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98 ; Write the equation by taking variation ... more

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220 ; Write the equation by taking variation ... more

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Parallel ; Non vertical lines can be parallel if ... more

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Zero ; Zero of a function is that value of for ... more

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Relative minimum ; Relative minimum is that value ... more

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Odd function ; A function is said to be an odd ... more

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Inverse variation ; An equation is said to be in ... more

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is a direct variation becausewhich is of the form... more

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; ; Write the equation by taking variation ... more

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is directly proportional to the square of and ... more

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; An equation of the form represents that and ... more

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The greatest integer function, , takes each input ... more

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The domain of may not be necessarily equal to the... more

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The graph of the function is the graph of the ... more

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The graph of is the graph of,which is reflected ... more

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Increasing:; decreasing:; relative minimum: at ; ... more

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Increasing:; decreasing:; relative maximum: 2 at... more

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; As two of the sides are feet each, the third ... more

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;  Observe the given diagram. The length of the ... more

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Substitute different values of from the interval... more

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Substitute different values of  from the interval... more

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The denominator of the expression is nonzero for.... more

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The greatest integer function gives each output as... more

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The greatest integer function gives each output as... more

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; ; ; ; As lies in the interval , so use the ... more

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; ; ; ; As , so use the formula to evaluate.... more

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; The domain of the function is the interval ... more

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; The expression inside the square root must be ... more

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Does not exist ; The expression inside the square ... more

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; The profit,, is the difference between revenue ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function and ... more

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; Substitute for into the given function and ... more

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9 ; Substitute 1 for into the equation, . ; ... more

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5 ; Substitute 1 for into the equation, . ; ... more

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128 ; Substitute for into the equation, . ; ... more

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580 ; Substitute 3 for into the equation, . ; ... more

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7 ; Substitute for into the equation, . ; ... more

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; Substitute 2 for into the equation, . ; ... more

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; Substitute the given value of into the ... more

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; Substitute the given value of into the ... more

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, ; is the function whose power is raised to .... more

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, ; The function , ,  is raised to power 2 and is ... more

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-axis: yes; -axis: yes; origin: yes ; Plot the ... more

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-axis: yes; -axis: yes; origin: yes ; Plot the ... more

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-axis: no; -axis: no; origin: no ; Plot the graph ... more

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-axis: no; -axis: yes; origin: no ; Plot the graph... more

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-axis: no; -axis: no; origin: yes ; Plot the graph... more

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-axis: no; -axis: yes; origin: no ; Plot the graph... more

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In question 46, observe the graph to check the ... more

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Replace with in the function and simplify. ... more

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; The graph of is the graph of shifted to the ... more

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; The graph of is the graph of shifted to the ... more

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; The graph of is the graph of stretching ... more

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The graph of is the graph of the function,, ... more

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Since, the graph of can be obtained by horizontal ... more

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 Since , the graph of can be obtained from the ... more

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The graph of is the graph of the function,, ... more

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; Write the equation by taking the variation ... more

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; Write the equation by taking the variation ... more

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; Write the equation by taking the variation ... more

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; Write the equation by taking the variation ... more

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; Write the equation by assuming that varies ... more

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; Write the equation by assuming that varies ... more

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20 min ; Write the equation by taking the ... more

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75 ; Write the equation of direct variation by ... more

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500 watts ; Write the equation of direct variation... more

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The domain of is all real numbers that is .The ... more

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To transform the graph of to the right by units... more

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The graph of is the graph of , compressed ... more

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Entire Proof Answer:  ; Assumptions: Let and be ... more

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The graph of is obtained by reflecting the graph ... more

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The graph of is obtained by horizontally ... more

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Symmetric with respect to the -axis, the -axis, ... more

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Following are the natures of the polynomial ... more

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Doubling causes to be quadrupled. ; Write the ... more

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varies inversely as . ; Write the equation of ... more

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Increasing:; decreasing:; relative maximum: 2 at... more

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; According to the given conditions, the height ... more

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Substitute different values of from the interval... more

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; ; ; As lies in the interval , use the formula ... more

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66 ; The domain of and is and , respectively.As... more

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6 ; The domain of and is and respectively.As ... more

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; The domain of the function is the set of real ... more

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0 ; The domain of the function is the set of real... more

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; The domain of a function is the set of all ... more

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; For x to be real, the expression under the ... more

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; The domain of a function is the set of all ... more

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; The domain of a function is the set of all ... more

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; The domain of a function is the set of all ... more

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; The domain of a function is the set of all ... more

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; Substitute for and for into the function. ; ... more

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; Substitute for and for into the function. ; ... more

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; Substitute for and for into the function. ; ... more

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; Substitute for and for into the function. ; ... more

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; Substitute x + h for x into. ; Substitute for... more

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; Substitutefor into the given function.Use the ... more

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; Substitute 2 for into the equation, . ; ... more

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0 ; Substitute for into the equation, . ; ... more

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4 ; Substitute 1 for into the equation, . ; ... more

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; Substitute the given value of into the ... more

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; ; Substitute the given value of into the ... more

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; ; Substitute the given value of into the ... more

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, ;   is the function whose power is raised to 5.... more

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-axis: no; -axis: yes; origin: no ; Replace y with... more

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Odd ; Replace with in the given function and ... more

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; The graph of is the graph of shifted to the ... more

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; The graph of is the graph of shifted to the ... more

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Since , the graph of is obtained by vertically ... more

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; Write the equation of inverse variation by ... more

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; Write the equation by choosing the variation ... more

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50 ft ; Write the equation of variation by ... more

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; Since , the graph of is obtained by ... more

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