Test Bank for Calculus: Early Transcendentals, 3rd Edition

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ExamName___________________________________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)FunctionB)Not a function2)2)A)FunctionB)Not a function3)3)A)FunctionB)Not a function1

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4)4)A)FunctionB)Not a function5)5)A)FunctionB)Not a function6)6)A)FunctionB)Not a functionFind the domain and graph the function.2

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7)f(x)=3x-67)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+2x-x28)A)D: (-Q,Q)B)D: (-Q,Q)C)D: (-Q,3]D)D: (-Q,Q)4

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9)F(x)=-x9)A)D: (-Q, 0)B)D: [0,Q)C)D: (-Q, 0]D)D: (-Q,Q)5

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10)G(x)=x10)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-1t-111)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)=1t+312)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-x213)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)=t2+514)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-z15)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+x16)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)=1t17)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)=-10z+118)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)=102+x19)A)D: (-Q,Q), R:0,5B)D: [0,Q), R:0,5C)D: [0,Q), R:(-Q,Q)D)D: (-Q,0], R:(-Q,0]20)F(t)=34t20)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-z221)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 of9feet and a height of65feet is filled to a height of h. Thevolume V of water (in cubic feet) is given by the function g(h)=81Δh.22)A)D=[0,5265Δ]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 bythe functionf(r)=43Δr3. Assume the balloon can hold up to4m3of air.23)A)D=[0,4]The independent variable is r.The dependent variable is V.B)D=33Δ,4The independent variable is r.The dependent variable is V.C)D=0,3Δ3The independent variable is V.The dependent variable is r.D)D=0,33ΔThe independent variable is r.The dependent variable is V.Solve the problem.24)If f(x)=5x+7and g(x)=2x-1, find f(g(x)).24)A)10x+13B)10x+2C)10x+6D)10x+1225)If f(x)=-5x+9and g(x)=4x+8, find g(f(x)).25)A)-20x+44B)-20x-28C)-20x+49D)20x+4426)If f(x)=x-47and g(x)=7x+4, find g(f(x)).26)A)7x+24B)x+8C)xD)-4727)If f(x)=x+8and g(x)=8x-12, find f(g(x)).27)A)22x+1B)22x-1C)8x-4D)8x+8-1228)If f(x)=4x2+2x+7and g(x)=2x-8, find g(f(x)).28)A)4x2+4x+6B)4x2+2x-1C)8x2+4x+22D)8x2+4x+629)If f(x)=1xand g(x)=3x5, find g(f(x)).29)A)13x5B)1x5C)3xD)3x530)If f(x)=-3x+8and g(x)=-5x2+3x-8,find g(f(-5)).30)A)-54B)-2584C)2D)45231)If f(x)=-5x+8and g(x)=6x2-5x+5,find g(f(8)).31)A)-1737B)-57C)-27D)630932)If f(x)=x, g(x)=x3, and h(x)=3x+9, find f(g(h(x))).32)A)x+9B)3x+9C)x+3D)x+310

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33)If f(x)=x, g(x)=x5, and h(x)=5x+20, find h(g(f(x))).33)A)5x+20B)x+4C)x+4D)x+20Express the given function as a composite of functions f and g such that y=f(g(x)).34)y=1x2-834)A)f(x)=1x2, g(x)=x-8B)f(x)=18, g(x)=x2-8C)f(x)=1x, g(x)=x2-8D)f(x)=1x2, g(x)=-1835)y=9x+435)A)f(x)=x, g(x)=9x+4B)f(x)=-x, g(x)=9x+4C)f(x)=-x, g(x)=9x-4D)f(x)=x, g(x)=9x+436)y=5x2+636)A)f(x)=1x, g(x)=5x+6B)f(x)=x+6, g(x)=5x2C)f(x)=5x2, g(x)=6D)f(x)=x, g(x)=5x+637)y=55x+137)A)f(x)=5x+1, g(x)=5B)f(x)=5x, g(x)=5x+1C)f(x)=5, g(x)=5+1D)f(x)=5x, g(x)=5x+138)y=(3x+13)738)A)f(x)=3x7, g(x)=x+13B)f(x)=(3x)7, g(x)=13C)f(x)=x7, g(x)=3x+13D)f(x)=3x+13, g(x)=x7Solve the problem.39)Let f(x)=xx-6. Find a function y=g(x) so that (fHg)(x)=x.39)A)g(x)=6xx-1B)g(x)=1x-6C)g(x)=x-66D)g(x)=x(x-6)40)Let f(x)=x-4. Find a function y=g(x) so that (fHg)(x)=x2-4.40)A)g(x)=x2B)g(x)=x2-4C)g(x)=x2+4D)g(x)=2x11

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41)Let g(x)=x. Find a function y=f(x) so that (fHg)(x)=x.41)A)f(x)=x2B)f(x)=1xC)f(x)=xD)f(x)=1x242)Let g(x)=x+2. Find a function y=f(x) so that (fHg)(x)=4x+842)A)f(x)=4(x+1)B)f(x)=4xC)f(x)=4x-2D)f(x)=4x+2Simplify the difference quotientsf(x+h)-f(x)handf(x)-f(a)x-afor the following function. Rationalize the numeratorwhen necessary.43)f(x)=7x+143)A)7x-7h;7x-7aB)7h;7aC)7;7D)7;7x-7a44)f(x)=3x44)A)6x+h;6x-aB)-3x+h;-3x-aC)6x(x+h);6axD)-3x(x+h);-3ax45)f(x)=6x345)A)18x2-18x-6h;6x2-6ax-6a2B)18x2+18xh+6h2;6x2+6ax+6a2C)6x2+6xh+6h2;18x2+18ax+18a2D)6x2+6xh+6h2;6x2+18ax+18a246)f(x)=2x2+7x-546)A)4x+2h+7;2x+2a+7B)4x+7h-5;4x+4a+7C)4x+4h+7;2x-2a-7D)4x2+h;4x+4a+747)f(x)=xx+347)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)=1-2x48)A)12x+2h+1-2x+1;12x+1-2a+1B)21-2x-2h+1-2x;22x-1+2a-1C)-21-2x-2h+1-2x;-21-2x+1-2aD)-11-2x-2h-1-2x;-11-2x-1-2a12

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49)f(x)=-8x49)A)8x(x+h)-xx+h;8xa-axB)8x(x+h)+xx+h;8xa+axC)8xx+h-x(x+h);8ax-xaD)-8x(x+h)+xx+h;-8xa+axGraph the function. Determine the symmetry, if any, of the function.50)y=1x350)A)Symmetric about the originB)No symmetry13

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C)Symmetric about the y-axisD)Symmetric about the origin51)y=-1x251)A)Symmetric about the y-axisB)Symmetric about the y-axis14

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C)No symmetryD)Symmetric about the y-axis52)y=1x52)A)Symmetric about the originB)Symmetric about the origin15

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