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Test Bank for Calculus: Early Transcendentals, 3rd Edition

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    Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the graph is a graph of a function of x. 1) 1) A) Function B) Not a function 2) 2) A) Function B) Not a function 3) 3) A) Function B) Not a function 1

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    4) 4) A) Function B) Not a function 5) 5) A) Function B) Not a function 6) 6) A) Function B) Not a function Find the domain and graph the function. 2

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    7) f(x) = 3 x - 6 7) A) D: [0 , Q ) B) D: ( - Q , Q ) C) D: ( - Q , Q ) D) D: ( - Q , Q ) 3

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    8) g(x) = 2 + 2 x - x 2 8) A) D: ( - Q , Q ) B) D: ( - Q , Q ) C) D: ( - Q , 3 ] D) D: ( - Q , Q ) 4

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    9) F(x) = - x 9) A) D: ( - Q , 0) B) D: [0, Q ) C) D: ( - Q , 0] D) D: ( - Q , Q ) 5

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    10) G(x) = x 10) A) D: [0, Q ) B) D: ( - Q , 0] C) D: ( - Q , 0) D) D: ( - Q , Q ) 6

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    11) F(t) = t - 1 t - 1 11) A) D: ( - Q , Q ) B) D: ( - Q , 1 ) 1 ( 1 > , Q ) C) D: ( - Q , 1 ) 1 ( 1 , Q ) D) D: ( - Q , 0) 1 (0, Q ) 7

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    12) G(t) = 1 t + 3 12) A) D: ( - Q , - 3 ) 1 ( - 3 , Q ) B) D: ( - Q , 0) 1 (0, Q ) C) D: ( - Q , - 3 ) 1 ( - 3 , Q ) D) D: ( - Q , Q ) Find the domain and range of the function. 13) f(x) = 4 - x 2 13) A) D: ( - Q , Q ), R: [ 4 , Q ) B) D: ( - Q , Q ), R: ( - Q , Q ) C) D: ( - Q , 4 ], R: ( - Q , Q ) D) D: ( - Q , Q ), R: ( - Q , 4 ] 8

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    14) F(t) = t 2 + 5 14) A) D: ( - Q , Q ), R: ( - Q , Q ) B) D: ( - Q , Q ), R: [ 5 , Q ) C) D: [0, Q ), R: ( - Q , 5 ] D) D: [ - 25 , Q ) , R: [ 5 , Q ) 15) g(z) = - 5 - z 15) A) D: ( - Q , Q ), R: ( - Q , - 5 ] B) D: ( - Q ,0], R: [ - 5 , Q ) C) D: ( - Q , - 5 ] , R: ( - Q , Q ) D) D: [0, Q ), R: ( - Q , - 5 ] 16) f(x) = 7 + x 16) A) D: [0, Q ), R: [ 7 , Q ) B) D: [0, Q ), R: ( - Q , Q ) C) D: ( - Q , Q ), R: [ 7 , Q ) D) D: ( - Q ,0], R: ( - Q , 7 ] 17) F(t) = 1 t 17) A) D: ( - Q ,0) , R: ( - Q ,0) B) D: [0, Q ) , R: ( - Q , Q ) C) D: (0, Q ) , R: (0, Q ) D) D: ( - Q , Q ) , R: ( - Q , Q ) 18) g(z) = - 10 z + 1 18) A) D: [1 , Q ) , R: ( - Q , Q ) B) D: ( - 1, Q ) , R: ( - Q ,0) C) D: [0, Q ), R: ( - Q , Q ) D) D: ( - Q , - 1) , R: (0, Q ) 19) f(x) = 10 2 + x 19) A) D: ( - Q , Q ) , R: 0, 5 B) D: [0, Q ) , R: 0, 5 C) D: [0, Q ) , R: ( - Q , Q ) D) D: ( - Q ,0] , R:( - Q ,0] 20) F(t) = 3 4 t 20) A) D: ( - Q ,0) , R: ( - Q ,0) B) D: (0, Q ) , R: (0, Q ) C) D: [0, Q ) , R: [0, Q ) D) D: ( - Q , Q ) , R: ( - Q , Q ) 21) g(z) = 25 - z 2 21) A) D: [ - 5 , 5 ], R: [0, 5 ] B) D: ( - Q , Q ) , R: (0, 5 ) C) D: ( - 5 , 5 ), R: ( - 5 , 5 ) D) D: [0, Q ), R: ( - Q , Q ) Determine an appropriate domain of the function. Identify the independent and dependent variables. 22) A cylindrical water tank with a radius of 9 feet and a height of 65 feet is filled to a height of h. The volume V of water (in cubic feet) is given by the function g(h) = 81 Δ h. 22) A) D = [0, 5265 Δ ] The independent variable is V. The dependent variable is h. B) D = [0, 65 ] The independent variable is V. The dependent variable is h. C) D = [0, 81 ] The independent variable is h. The dependent variable is V. D) D = [0, 65 ] The independent variable is h. The dependent variable is V. 9

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    23) A weather balloon of radius r (in meters) is filled with air. The volume V of the balloon is given by the function f(r) = 4 3 Δ r 3 . Assume the balloon can hold up to 4 m 3 of air. 23) A) D = [0, 4 ] The independent variable is r. The dependent variable is V. B) D = 3 3 Δ , 4 The independent variable is r. The dependent variable is V. C) D = 0, 3 Δ 3 The independent variable is V. The dependent variable is r. D) D = 0, 3 3 Δ The independent variable is r. The dependent variable is V. Solve the problem. 24) If f(x) = 5 x + 7 and g(x) = 2 x - 1, find f(g(x)). 24) A) 10 x + 13 B) 10 x + 2 C) 10 x + 6 D) 10 x + 12 25) If f(x) = - 5 x + 9 and g(x) = 4 x + 8 , find g(f(x)). 25) A) - 20 x + 44 B) - 20 x - 28 C) - 20 x + 49 D) 20 x + 44 26) If f(x) = x - 4 7 and g(x) = 7 x + 4 , find g(f(x)). 26) A) 7 x + 24 B) x + 8 C) x D) - 4 7 27) If f(x) = x + 8 and g(x) = 8x - 12 , find f(g(x)). 27) A) 2 2 x + 1 B) 2 2 x - 1 C) 8 x - 4 D) 8 x + 8 - 12 28) If f(x) = 4x 2 + 2 x + 7 and g(x) = 2 x - 8 , find g(f(x)). 28) A) 4x 2 + 4 x + 6 B) 4x 2 + 2 x - 1 C) 8 x 2 + 4 x + 22 D) 8 x 2 + 4 x + 6 29) If f(x) = 1 x and g(x) = 3 x 5 , find g(f(x)). 29) A) 1 3 x 5 B) 1 x 5 C) 3 x D) 3 x 5 30) If f(x) = - 3 x + 8 and g(x) = - 5 x 2 + 3 x - 8 , find g( f ( - 5 )). 30) A) - 54 B) - 2584 C) 2 D) 452 31) If f(x) = - 5 x + 8 and g(x) = 6 x 2 - 5 x + 5 , find g( f( 8 )). 31) A) - 1737 B) - 57 C) - 27 D) 6309 32) If f(x) = x , g(x) = x 3 , and h(x) = 3 x + 9 , find f(g(h(x))). 32) A) x + 9 B) 3 x + 9 C) x + 3 D) x + 3 10

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    33) If f(x) = x , g(x) = x 5 , and h(x) = 5 x + 20 , find h(g(f(x))). 33) A) 5 x + 20 B) x + 4 C) x + 4 D) x + 20 Express the given function as a composite of functions f and g such that y = f(g(x)). 34) y = 1 x 2 - 8 34) A) f(x) = 1 x 2 , g(x) = x - 8 B) f(x) = 1 8 , g(x) = x 2 - 8 C) f(x) = 1 x , g(x) = x 2 - 8 D) f(x) = 1 x 2 , g(x) = - 1 8 35) y = 9 x + 4 35) A) f(x) = x, g(x) = 9 x + 4 B) f(x) = - x , g(x) = 9 x + 4 C) f(x) = - x , g(x) = 9 x - 4 D) f(x) = x , g(x) = 9 x + 4 36) y = 5 x 2 + 6 36) A) f(x) = 1 x , g(x) = 5 x + 6 B) f(x) = x + 6 , g(x) = 5 x 2 C) f(x) = 5 x 2 , g(x) = 6 D) f(x) = x, g(x) = 5 x + 6 37) y = 5 5 x + 1 37) A) f(x) = 5 x + 1 , g(x) = 5 B) f(x) = 5 x , g(x) = 5 x + 1 C) f(x) = 5 , g(x) = 5 + 1 D) f(x) = 5 x , g(x) = 5 x + 1 38) y = ( 3 x + 13 ) 7 38) A) f(x) = 3 x 7 , g(x) = x + 13 B) f(x) = ( 3 x) 7 , g(x) = 13 C) f(x) = x 7 , g(x) = 3 x + 13 D) f(x) = 3 x + 13 , g(x) = x 7 Solve the problem. 39) Let f(x) = x x - 6 . Find a function y = g(x) so that (f H g)(x) = x. 39) A) g(x) = 6 x x - 1 B) g(x) = 1 x - 6 C) g(x) = x - 6 6 D) g(x) = x(x - 6 ) 40) Let f(x) = x - 4 . Find a function y = g(x) so that (f H g)(x) = x 2 - 4 . 40) A) g(x) = x 2 B) g(x) = x 2 - 4 C) g(x) = x 2 + 4 D) g(x) = 2x 11

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    41) Let g(x) = x . Find a function y = f(x) so that (f H g)(x) = x . 41) A) f(x) = x 2 B) f(x) = 1 x C) f(x) = x D) f(x) = 1 x 2 42) Let g(x) = x + 2 . Find a function y = f(x) so that (f H g)(x) = 4 x + 8 42) A) f(x) = 4 (x + 1) B) f(x) = 4 x C) f(x) = 4 x - 2 D) f(x) = 4 x + 2 Simplify the difference quotients f(x + h) - f(x) h and f(x) - f(a) x - a for the following function. Rationalize the numerator when necessary. 43) f(x) = 7 x + 1 43) A) 7 x - 7 h; 7 x - 7 a B) 7 h; 7 a C) 7 ; 7 D) 7 ; 7 x - 7 a 44) f(x) = 3 x 44) A) 6 x + h ; 6 x - a B) - 3 x + h ; - 3 x - a C) 6 x(x + h) ; 6 ax D) - 3 x(x + h) ; - 3 ax 45) f(x) = 6 x 3 45) A) 18 x 2 - 18 x - 6 h; 6 x 2 - 6 ax - 6 a 2 B) 18 x 2 + 18 xh + 6 h 2 ; 6 x 2 + 6 ax + 6 a 2 C) 6 x 2 + 6 xh + 6 h 2 ; 18 x 2 + 18 ax + 18 a 2 D) 6 x 2 + 6 xh + 6 h 2 ; 6 x 2 + 18 ax + 18 a 2 46) f(x) = 2 x 2 + 7 x - 5 46) A) 4 x + 2 h + 7 ; 2 x + 2 a + 7 B) 4 x + 7 h - 5 ; 4 x + 4 a + 7 C) 4 x + 4 h + 7 ; 2 x - 2 a - 7 D) 4 x 2 + h; 4 x + 4 a + 7 47) f(x) = x x + 3 47) A) 1 ( 3 - x)( 3 - x - h) ; 1 ( 3 - x)( 3 - a) B) 3 (x + 3 )(x + h + 3 ) ; 3 (x + 3 )(a + 3 ) C) - 3 ( 3 - x)( 3 - x - h) ; - 3 ( 3 - x)( 3 - a) D) - h + 3 (x + 3 )(x + h + 3 ) ; - a + 3 (x + 3 )(a + 3 ) 48) f(x) = 1 - 2 x 48) A) 1 2 x + 2 h + 1 - 2 x + 1 ; 1 2 x + 1 - 2 a + 1 B) 2 1 - 2 x - 2 h + 1 - 2 x ; 2 2 x - 1 + 2 a - 1 C) - 2 1 - 2 x - 2 h + 1 - 2 x ; - 2 1 - 2 x + 1 - 2 a D) - 1 1 - 2 x - 2 h - 1 - 2 x ; - 1 1 - 2 x - 1 - 2 a 12

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    49) f(x) = - 8 x 49) A) 8 x (x + h) - x x + h ; 8 x a - a x B) 8 x (x + h) + x x + h ; 8 x a + a x C) 8 x x + h - x (x + h) ; 8 a x - x a D) - 8 x (x + h) + x x + h ; - 8 x a + a x Graph the function. Determine the symmetry, if any, of the function. 50) y = 1 x 3 50) A) Symmetric about the origin B) No symmetry 13

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    C) Symmetric about the y - axis D) Symmetric about the origin 51) y = - 1 x 2 51) A) Symmetric about the y - axis B) Symmetric about the y - axis 14

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    C) No symmetry D) Symmetric about the y - axis 52) y = 1 x 52) A) Symmetric about the origin B) Symmetric about the origin 15

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