Q: Which of the following best describes the graph of $y = |x - 3|$?

A V-shaped graph with vertex at $(3, 0)$

Q: Which of the following is the domain of the function $f(x) = \frac{1}{x - 4}$?

All real numbers except $x = 4$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

Given the function $f(x) = 2x^2 - 3x + 5$, what is $f(-2)$?

Accepted Answer

$f(-2) = 17$

Question 3

Which of the following equations represents a line with a slope of $-3$ and a $y$-intercept of $4$?

Accepted Answer

$y = -3x + 4$

Question 4

A chemical reaction's temperature $T$ (in degrees Celsius) is modeled by $T(t) = 5t^2 + 2t + 20$, where $t$ is time in hours. What is the temperature after 3 hours?

Accepted Answer

$T(3) = 59$

Question 5

Which of the following is the solution set for the inequality $2x - 5 < 9$?

Accepted Answer

$x < 7$

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $P$ after $t$ hours?

Accepted Answer

$P(t) = 200 \cdot 3^{t/4}$

Question 7

Solve for $x$: $\frac{2x - 1}{3} = 5$

Accepted Answer

$x = 8$

Question 8

Which of the following is the vertex of the parabola $y = (x - 2)^2 + 5$?

Accepted Answer

$(2, 5)$

Question 9

A medication's concentration in the bloodstream is modeled by $C(t) = 50e^{-0.2t}$, 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 10

Which of the following is the solution to the quadratic equation $x^2 - 6x + 8 = 0$?

Accepted Answer

$x = 2$ and $x = 4$

Question 11

A car rental company charges a flat fee of $\$30$ plus $\$0.20$ per mile driven. Which equation models the total cost $C$ for $m$ miles?

Accepted Answer

$C = 30 + 0.20m$

Question 12

Which of the following is the inverse of the function $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \frac{x + 7}{3}$

Question 13

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(2)$?

Accepted Answer

$(f \circ g)(2) = 9$

Question 14

Which of the following best describes the graph of $y = |x - 3|$?

Accepted Answer

A V-shaped graph with vertex at $(3, 0)$

Question 15

A student invests $\$1000$ in an account that earns $6\%$ annual interest compounded yearly. Which formula gives the amount $A$ after $t$ years?

Accepted Answer

$A = 1000(1.06)^t$

Question 16

Which of the following is the solution to the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3, y = 1$

Question 17

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

Accepted Answer

All real numbers except $x = 4$

Question 18

A rectangle has a length that is 3 times its width. If the perimeter is 64 units, what is the area?

Accepted Answer

192 square units

Question 19

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

Accepted Answer

$x = 32$

Question 20

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $t$ seconds is given by $h(t) = -4.9t^2 + 10t + 2$. What is the maximum height reached by the ball?

Accepted Answer

7.1 meters

College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards