e e Correct Answer 1 1 undefined You Answered ln4 ln4 Evaluate g2 g2 then

E e correct answer 1 1 undefined you answered ln4 ln4

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e e Correct Answer 0 0 1 1 undefined You Answered ln4 ln4
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Evaluate g(2) g(2), then evaluate f(g(2)) f(g(2)). g(2)f(g(2))=2 2 −3−−−− −√=1=f(1)=ln1=0. g(2)=22−3=1f(g(2))=f(1)=ln1=0. Question 6 1.67 / 1.67 pts Suppose two quantities q q and x x are inversely proportional. Choose the expression below that could represent this relationship. q=3x q=3x q=−3x q=−3x qx =3 qx=3 Correct! q= 3x q=3x q=3x 12 q=3x12 If q q is inversely proportional to x x, then for some constant k k, qq=k⋅1x=kx q=k 1xq=kx Question 7 1.66 / 1.66 pts
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Choose the statement below that is FALSE. Correct! If x>0 x>0 and k>0 k>0 , then ln(kx)=kln(x) ln(kx)=kln(x) ln(e x )=x ln(ex)=x If x>0 x>0 then ln(x k )=kln(x) ln(xk)=kln(x) If x>0 x>0 then e lnx =x elnx=x If A>0 A>0 and B>0 B>0 then ln AB =ln(A)−ln(B) lnAB=ln(A)−ln(B) ln(kx)≠kln(x) ln(kx)≠kln(x). Question 8 0 / 1.66 pts Choose the periodic function that matches the graph shown below: Correct Answer
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20sin(2x)+10 20sin(2x)+10 You Answered 20sin(x)+10 20sin(x)+10 30cos(2x) 30cos(2x) 40sin(x)−10 40sin(x)−10 10cos(2x)+10 10cos(2x)+10 The graph shows two cycles of sine, with amplitude 20 20. The period is π π, so B= 2ππ =2 B=2ππ=2. There is a vertical shift of 10 10. Therefore the equation is 20sin(2x)+10. 20sin(2x)+10. Question 9 1.66 / 1.66 pts Calculate the amplitude and period of the function: f(t)=−cos(3t)− 12 f(t)=−cos(3t)−12 Amplitude: 12 12 , period: 3 3 .
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Amplitude: 1 1 , period: 13 13 . Amplitude: 2 2 , period: . Correct! Amplitude: 1 1 , period: 2π3 2π3 . Amplitude: 1 1 , period: π3 π3 . The function Asin(Bt)+C Asin(Bt)+C has amplitude |A| |A| and period 2π|B| 2π|B|. The amplitude is 1 1, the period is 2π3 2π3. Question 10 1.67 / 1.67 pts Which of the following functions is not a power function? Correct! x 2 +e x x2+ex x 1.3 7 x1.37 7x 4 7x4
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9x 1.4 9x1.4 2⋅x 32 2 x32 The function x 2 +e x x2+ex is a combination of a power function and an exponential- and so is not a power function. Question 11 0 / 1.67 pts Which of the following functions is not a power function? Correct Answer 3⋅2 x 3 2x 3x−−√ 3x You Answered 2⋅(x 23 ) 15 2 (x23)15 2x 3 2x3 4x√ 4x The function 5⋅2 x 5 2x is an exponential function. All the others are power functions and can be expressed in the form k⋅x p k xp for some p p.
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Question 12 0 / 1.66 pts Choose the statement below that is FALSE: The function f(x)=lnx f(x)=lnx is an increasing function. The value of ln(1) ln(1) is 0 0 . The function f(x)=lnx f(x)=lnx is not defined for x≤0 x≤0 . Correct Answer The function f(x)=lnx f(x)=lnx is a decreasing function. You Answered The value of ln(e 2 ) ln(e2) is 2 2 . The function f(x)=lnx f(x)=lnx is increasing, not decreasing. Here is a plot of the graph of lnx lnx.
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Question 13 1.67 / 1.67 pts Use the table below to calculate g(f(2)) g(f(2)) x -1 0 1 2 3 4 5 f(x) 1 0 1 4 9 16 25 g(x ) 10 6 3 1 -1 -3 -6 4 16 1 3 Correct! -3
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f(2)=4 f(2)=4. g(4)=−3 g(4)=−3.
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