Question 1

Which of the following is the domain of the rational function $f(x) = \frac{2x+1}{x^2-4}$?

Accepted Answer

$x 
eq 2,\ x 
eq -2$

Question 2

A medical dosage formula is given by $D(t) = \frac{100}{t-3}$, where $t$ is the time in hours after administration. What is the vertical asymptote of $D(t)$?

Accepted Answer

$t = 3$

Question 3

Given the function $f(x) = 3x + 5$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{3}$

Question 4

Which of the following graphs represents an exponential growth function?

Accepted Answer

$y = 4^x$

Question 5

A population of bacteria doubles every 3 hours. Which equation models the population $P$ after $t$ hours, if the initial population is $P_0$?

Accepted Answer

$P = P_0 \cdot 2^{t/3}$

Question 6

Which property of logarithms allows you to write $\log_b(xy)$ as $\log_b(x) + \log_b(y)$?

Accepted Answer

Product property

Question 7

Expand the logarithmic expression $\log_2(8x)$ using properties of logarithms.

Accepted Answer

$\log_2(8) + \log_2(x)$

Question 8

Solve for $x$: $2^x = 16$.

Accepted Answer

$x = 4$

Question 9

A scientist measures the pH of a solution as $pH = -\log_{10}[H^+]$. If $[H^+] = 1 	imes 10^{-5}$, what is the pH?

Accepted Answer

$pH = 5$

Question 10

Which of the following is the correct inverse of the exponential function $f(x) = e^{2x}$?

Accepted Answer

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

Question 11

Which of the following is equivalent to $\log_5(125)$?

Accepted Answer

$3$

Question 12

If $f(x) = \frac{1}{x-1}$, which value of $x$ makes $f(x)$ undefined?

Accepted Answer

$x = 1$

Question 13

Which of the following is the correct solution to $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 14

A radioactive substance decays according to $A(t) = A_0 e^{-0.2t}$. What is the half-life of the substance?

Accepted Answer

$t = \frac{\ln(2)}{0.2}$

Question 15

Which of the following is the correct application of the change of base formula for $\log_7(50)$?

Accepted Answer

$\frac{\log_{10}(50)}{\log_{10}(7)}$

Question 16

Which of the following expressions is equivalent to $\ln(x^2y)$?

Accepted Answer

$2\ln(x) + \ln(y)$

Question 17

Solve for $x$: $\log_3(x-2) = 4$.

Accepted Answer

$x = 82$

Question 18

A car's value depreciates exponentially according to $V(t) = 20000 \cdot 0.85^t$, where $t$ is the number of years. What is the value after 3 years?

Accepted Answer

$20000 \cdot 0.85^3$

Question 19

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

Accepted Answer

$x = \ln(7)$

College Algebra Exam #3 Study Guide: Rational, Inverse, Exponential, and Logarithmic Functions

Study Guide - Practice Questions

Study Guide - Flashcards