Question 1

Which of the following best describes the domain of the function $$f(x) = \ln(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 2

Given the function $$f(x) = e$$^{x}$$, which of the following statements about its range is correct?

Accepted Answer

$$(0, \infty)$$

Question 3

If $$f(x) = \ln(x)$$ and $$g(x) = e$$^{x}$$, which of the following is true about their relationship?

Accepted Answer

$$f(g(x)) = x$$

Question 4

Which of the following is the correct graph for $$f(x) = \ln(x+1)$$?

Accepted Answer

A graph with a vertical asymptote at $$x = -1$$ and increasing for $$x \u003e -1$$

Question 5

Suppose a business models its revenue with $$R(x) = 100e$$^{0.05x}$$, where x$ is the number of months. What is the revenue after 12 months?

Accepted Answer

$$100e^{0.6}$$

Question 6

Which of the following is the correct inverse of the function $$f(x) = e$$^{x}$$?

Accepted Answer

$$f^{-1}(x$$) = \ln(x)$$

Question 7

A company’s cost function is $$C(x) = 50 + 20\ln(x)$$, where $$x is $$the number of units produced. What is the cost of producing 5 units?

Accepted Answer

$$50 + 20\ln(5)$$

Question 8

Which property of logarithms allows you to write $$\ln(ab) as$$ $$\ln(a) + \ln(b)$$?

Accepted Answer

Product property

Question 9

If $$f(x) = \ln(x)$$, what is the value of $$f(e^{3}$$)$$?

Accepted Answer

$$3$$

Question 10

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 11

Given $$f(x) = \ln(x)$$ and $$g(x) = \frac{1}{x}$$, which of the following is the domain of $$f(g(x))$$?

Accepted Answer

$$x \u003e 0$$

Question 12

Which of the following is the correct graph for $$f(x) = \frac{1}{x}$$?

Accepted Answer

A graph with vertical asymptote at $$x = 0$$ and horizontal asymptote at $$y = 0$$

Question 13

If $$f(x) = \ln(x)$$, which of the following is the correct transformation for $$f(x+2)$$?

Accepted Answer

Shift left by 2 units

Question 14

Which of the following is the correct property of exponential functions?

Accepted Answer

$$e^{a+b}$$ = $$e^{a}$$ \cdot $$e^{b}$$

Question 15

If $$f(x) = \ln(x)$$, what is the vertical asymptote of its graph?

Accepted Answer

$$x = 0$$

Question 16

A company’s profit function is $$P(x) = 200e$$^{0.03x}$$ - 100$$, where $$x is $$the number of products sold. What is the profit when $$x = 10$$?

Accepted Answer

$$200e^{0.3} - 100$

Question 17

Which of the following is the correct property of logarithms?

Accepted Answer

$$\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)$$

Question 18

If $$f(x) = e$$^{x}$$, which of the following is the correct transformation for f(x-2$$)$$?

Accepted Answer

Shift right by 2 units

Question 19

Which of the following is the correct range for the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 20

If $$f(x) = \ln(x)$$, which of the following is the correct property for $$\ln(x$$^{a}$$)$$?

Accepted Answer

$$\ln(x$$^{a}$$) = a\ln(x)$$

Functions, Exponential and Logarithmic Functions in Business Calculus

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