Question 1

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

Accepted Answer

$x > 2$

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 $x > -1$

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

$x > 0$

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

Study Guide - Practice Questions