Question 1

Which of the following is the correct equation for the vertical asymptote of the function $f(x) = \frac{3x-2}{x^2-4}$?

Accepted Answer

$x = 2$ and $x = -2$

Question 2

Given the function $f(x) = \sqrt{x-1}$, what is the domain of $f$?

Accepted Answer

$[1, \infty)$

Question 3

Which of the following best describes the horizontal asymptote of $f(x) = \frac{3x-2}{x^2-4}$?

Accepted Answer

$y = 0$

Question 4

Suppose the population of a bacteria culture triples every 10 hours. Which equation models the population $P$ after $t$ hours, if the initial population is $P_0$?

Accepted Answer

$P = P_0 \cdot 3^{t/10}$

Question 5

Which of the following is the correct inverse of $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{2}$

Question 6

Evaluate $\log_2 32$ without a calculator.

Accepted Answer

$5$

Question 7

Which of the following functions is one-to-one?

Accepted Answer

$f(x) = x^3$

Question 8

Rewrite $\ln\left(\frac{x^2}{y}\right)$ as a sum or difference of logarithms.

Accepted Answer

$2\ln x - \ln y$

Question 9

Solve for $x$: $2^{x+1} = 16$.

Accepted Answer

$x = 3$

Question 10

Which of the following is the correct expression for $\log_3 81$?

Accepted Answer

$4$

Question 11

If $f(x) = \frac{1}{x-2}$, which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $x = 2$.

Question 12

Which of the following is the correct expanded form of $\log_2(xy^3)$?

Accepted Answer

$\log_2 x + 3\log_2 y$

Question 13

Given $f(x) = x^2 - 4$, which of the following is the $x$-intercept?

Accepted Answer

$(2, 0)$ and $(-2, 0)$

Question 14

Which of the following is the correct solution to $\log_5 x = 3$?

Accepted Answer

$x = 125$

Question 15

If $f(x) = \frac{3x-2}{x^2-4}$, what is the $y$-intercept?

Accepted Answer

$(0, \frac{1}{2})$

Question 16

Which of the following is the correct solution for $e^{2x} = 7$?

Accepted Answer

$x = \frac{1}{2} \ln 7$

Question 17

Which of the following is the correct expanded form of $\ln\left(\frac{xy^2}{z^3}\right)$?

Accepted Answer

$\ln x + 2\ln y - 3\ln z$

Question 18

If $f(x) = x^2$, which of the following statements is true?

Accepted Answer

The function is not one-to-one.

Question 19

Which of the following is the correct solution for $\log_2(x-1) = 3$?

Accepted Answer

$x = 9$

Question 20

Which of the following is the correct solution for $\ln(x^2-1) = 0$?

Accepted Answer

$x = \pm \sqrt{2}$

College Algebra: Practice Problems on Functions, Asymptotes, and Logarithms

Study Guide - Practice Questions

Study Guide - Flashcards