Question 1

Which of the following is the correct definition of the domain of a function $f(x)$?

Accepted Answer

The set of all $x$ values for which $f(x)$ is defined.

Question 2

A chemical reaction's temperature $T$ (in degrees Celsius) is modeled by $T(t) = 5t + 20$, where $t$ is time in minutes. What is the temperature after 8 minutes?

Accepted Answer

$T(8) = 60$

Question 3

Which of the following graphs represents a function?

Accepted Answer

A graph where every $x$ value corresponds to exactly one $y$ value.

Question 4

Given the equation $y = 2x - 3$, what is the $y$-intercept?

Accepted Answer

$-3$

Question 5

A hospital records the number of patients $P$ as a function of time $t$ in hours: $P(t) = 12t + 5$. How many patients are there after 4 hours?

Accepted Answer

$P(4) = 29$

Question 6

Which of the following is the solution set for $2x + 5 = 13$?

Accepted Answer

$x = 4$

Question 7

If $f(x) = x^2 - 4x + 7$, what is $f(3)$?

Accepted Answer

$f(3) = 10$

Question 8

Which of the following is the correct solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3, y = 2$

Question 9

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. Which equation models the total cost $C$ for $m$ miles?

Accepted Answer

$C = 25 + 0.20m$

Question 10

Which of the following is the correct factorization of $x^2 - 9$?

Accepted Answer

$(x - 3)(x + 3)$

Question 11

If $g(x) = 2x^2 - 5x + 1$, what is the vertex of the parabola?

Accepted Answer

$(1.25, -2.125)$

Question 12

Which of the following is the solution to $\sqrt{x} = 5$?

Accepted Answer

$x = 25$

Question 13

A population of bacteria doubles every hour. If the initial population is $P_0 = 100$, what is the population after 3 hours?

Accepted Answer

$P = 800$

Question 14

Which of the following is the correct solution to $|x - 4| = 7$?

Accepted Answer

$x = 11$ or $x = -3$

Question 15

A medication's concentration $C$ in the bloodstream decreases exponentially: $C(t) = 50e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$C(5) \approx 18$

Question 16

Which of the following is the correct solution to $x^2 + 6x + 9 = 0$?

Accepted Answer

$x = -3$

Question 17

A business's profit $P$ is given by $P(x) = -2x^2 + 40x - 100$, where $x$ is the number of units sold. What is the maximum profit?

Accepted Answer

$P = 300$

Question 18

Which of the following is the correct solution to $3(x - 2) = 2x + 5$?

Accepted Answer

$x = 7$

Question 19

If $h(x) = \frac{1}{x}$, which value of $x$ is not in the domain of $h(x)$?

Accepted Answer

$x = 0$

College Algebra: Functions, Graphs, and Equations Study Guide

Study Guide - Practice Questions

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