Question 1

Which of the following best describes the relationship between the graphs of $$y = e^x$$ and $$y = \ln x as $$shown in the image?

Accepted Answer

They are symmetric with respect to the line $$y = x.$$

Question 2

In the image, which color most likely represents the graph of $$y = e^x$$?

Accepted Answer

The blue curve.

Question 3

Based on the image, what is the domain of the red curve, which represents $$y = \ln x$$?

Accepted Answer

$$(0, \infty)$$

Question 4

Which of the following statements is true about the intersection of the black line and the other two curves in the image?

Accepted Answer

The black line is the line $$y = x$$ and intersects both $$y = e^x$$ and $$y = \ln x at$$ $$x = 1.$$

Question 5

If the blue curve is $$y = e^x$$, what is its range?

Accepted Answer

$$(0, \infty)$$

Question 6

Which of the following is the correct derivative of the red curve, $$y = \ln x$$?

Accepted Answer

$$\frac{1}{x}$$

Question 7

Suppose the black line is $$y = x. $$Which of the following points is on all three graphs shown in the image?

Accepted Answer

$$(1, 1)$$

Question 8

Which of the following best describes the end behavior of the blue curve, $$y = e^x$$, as $$x 	o -\infty$$?

Accepted Answer

$$y 	o 0$$

Question 9

Which of the following best describes the end behavior of the red curve, $$y = \ln x$$, as $$x 	o 0^+$$?

Accepted Answer

$$y 	o -\infty$$

Question 10

If the blue curve is $$y = e^x$$ and the red curve is $$y = \ln x$$, which of the following statements is true?

Accepted Answer

The blue curve is the inverse of the red curve.

Derivatives of Exponential and Logarithmic Functions: Business Calculus Study Guide

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