Graph the equation. 8) y = 6x - 2

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1 Math 0 Chapter Practice set The actual test differs. Write the equation that results in the desired transformation. 1) The graph of =, verticall compressed b a factor of 0.7 Graph the equation. 8) = - Solve the problem. ) Suppose that the -intercepts of the graph of = f() are 7 and. What are the -intercepts of = f()? Match the correct function to the graph. ) Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 9) f() = ( + 1) + - A) = - B) = - C) = 1 - D) = + Solve the problem. ) Suppose that the function = f() is increasing on the interval (, ). Over what interval is the graph of = f( - 8) increasing? ) A rectangular sign is being designed so that the length of its base, in feet, is feet less than times the height, h. Epress the area of the sign as a function of h. Graph the equation. ) = 1 ) Suppose that the -intercepts of the graph of = f() are and 8. What are the -intercepts of = f( + 9)? 7) A farmer has 00 ards of fencing to enclose a rectangular garden. Epress the area A of the rectangle as a function of the width of the rectangle. What is the domain of A?

2 Write the equation of a sine function that has the given characteristics. 11) The graph of =, shifted 7 units to the right Does the graph represent a function that has an inverse function? 1) Find the ais of smmetr of the parabola defined b the given quadratic function. 1) f() = Solve the problem. 1) You have 7 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maimize the enclosed area. 1) Write an equation in standard form of the parabola that has the same shape as the graph of f() =, but which has a minimum of 8 at =. Determine whether the given quadratic function has a minimum value or maimum value. Then find the coordinates of the minimum or maimum point. 1) f() = ) f() = Find the ais of smmetr of the parabola defined b the given quadratic function. ) f() = 11( - ) + ) f() = + Find the inverse of the one-to-one function. ) f() = 7-1 Find the range of the quadratic function. 17) f() = 7 - ( + ) 18) f() = Does the graph represent a function that has an inverse function? ) Find the domain and range of the quadratic function whose graph is described. 19) The maimum is at = -1 Find the -intercept for the graph of the quadratic function. 0) + = ( + ) Find the inverse of the one-to-one function. ) f() = - 8 Find the domain of the indicated combined function. 7) Find the domain of (fg)() when f() = 8 + and g() = 9 -.

3 Given functions f and g, perform the indicated operations. 8) f() = 7-9, g() = Find f g. ) Given functions f and g, determine the domain of f + g. 9) f() = + 9, g() = - Given functions f and g, perform the indicated operations. 0) f() = 9 -, g() = - 8 Find f - g. 1) f() = + 9, g() = 9 - Find fg. Begin b graphing the standard quadratic function f() =. Then use transformations of this graph to graph the given function. ) h() = ( + ) - 8 Find and simplif the difference quotient f( + h) - f(), h 0 for the given function. h ) f() = Graph the function. ) f() = + if < 1-1 if Use the shape of the graph to name the function. ) - Evaluate the piecewise function at the given value of the independent variable. 7) f() = + if < - + if - ; f(-) Determine whether the given function is even, odd, or neither. 8) f() = + + 9) f() = +

4 Use the graph of the given function to find an relative maima and relative minima. 0) f() = Identif the intervals where the function is changing as requested. 1) Decreasing ) Constant Evaluate the function at the given value of the independent variable and simplif. ) f() = + + ; f(-) ) f() = + - ; f( - 1) Determine whether the equation defines as a function of. ) - = 7) = ) + = Give the domain and range of the relation. 9) {(11, -), (-, -7), (-, -), (-, )} ) Decreasing Graph the equation. 0) =

5 Graph the function. Label at least two points on the graph. 1) f() = - + if < - if Graph the equation. 9) = Find the -intercepts (if an) for the graph of the quadratic function. ) + = ( - ) Find and simplif the difference quotient f( + h) - f(), h 0 for the given function. h 0) f() = 1 8 Write the equation of a function that has the given characteristics. ) The graph of =, shifted 8 units upward ) The graph of =, shifted 8 units to the left Determine whether the equation defines as a function of. State wh or wh not. ) + = 9 Find the domain of the function. - 1) h() = - 1 Identif the intervals where the function is changing as requested. ) Increasing 8 ) = 7 Determine whether the given function is even, odd, or neither. Use logic, not a graph. 7) f() = ) f() = - -8 Find the inverse of the one-to-one function. ) f() = ( - ) ) f() = + 7

6 Find the domain and range of the quadratic function whose graph is described. ) The verte is (1, 1) and the graph opens down. Given functions f and g, perform the indicated operations. ) f() = +, g() = 1 - Find fg. The graph of a function f is given. Use the graph to answer the question. 7) Find the numbers, if an, at which f has a relative minimum. What are the relative minima? Write the equation that results in the desired transformation. 7) The graph of =, verticall stretched b a factor of 8 Find the -intercept for the graph of the quadratic function. 7) f() = ( - ) - 9 Determine whether the given quadratic function has a minimum value or maimum value. Then find the coordinates of the minimum or maimum point. 7) f() = - - Write a function. 7) Elissa wants to set up a rectangular dog run in her backard. She has feet of fencing to work with and wants to use it all. If the dog run is to be feet long, epress the area of the dog run as a function of. Evaluate the function at the given value of the independent variable and simplif. 8) f() = + - ; f(-) For the given functions f and g, find the indicated composition. 9) f() = +, g() = 7 (f g)() Suppose the point (, ) is on the graph of = f(). Find a point on the graph of the given function. 70) = f( + ) Given functions f and g, determine the domain of f + g. 71) f() = -, g() = +

7 Answer Ke Testname: 0CHVP 1) = 0.7 ) 7 and ) A ) (, 1) ) A(h) = -h + h ) - and -1 7) A() = ; { 0 < < 00} 8) ) ) ) = - 7 1) = 1 1) 9 ft b 9 ft 7

8 Answer Ke Testname: 0CHVP 1) f() = ( - ) + 8 1) maimum; -, 9 1) maimum; 1, ) (-, 7] 18) (-, ] 19) Domain: (-, ) Range: (-, ] 0) (0, 0) 1) Yes ) = ) = 0 ) f-1() = ) No ) f-1() = + 8 7) Domain: 9, 7-9 8) ) (-, ) or (, ) 0) + 1) ) ) Standard cubic function ) Standard quadratic function ) + h + 7 8

9 Answer Ke Testname: 0CHVP ) (1, ) - (1, -1) - 7) - 8) Neither 9) Even 0) minimum: (, -1); maimum: (-, 18) 1) (-, ) ) (-, -) ) (-, -1) or (, ) ) - 1 ) - - ) is a function of 7) is a function of 8) is a function of 9) domain = {11, -, -}; range = {-, -7, -, } 0)

10 Answer Ke Testname: 0CHVP 1) - - ) (0, 0) and (, 0) ) = + 8 ) = + 8 ) is a function of ) is not a function of 7) Neither 8) Odd 9) ) -1 8 ( + h) - 1) (-, -) (-, 0) (0, ) (, ) ) (0, ) ) f-1() = + ) f-1() = - 7 ) Domain: (-, ) Range: (-, 1] ) ( + )( 1 - ) 7) f has a relative minimum at = -1 and 1; the relative minimum is 0 8) ) 8 +

11 Answer Ke Testname: 0CHVP 70) (-, ) 71) (-, -) or (-, ) or (, ) 7) = 8 7) (0, 0) 7) minimum; 1, - 7) A() = 1-11