Question 1

Which of the following best describes the solution set of the equation $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ and $x = 3$

Question 2

A company’s profit $P$ (in thousands of dollars) is modeled by the function $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $18$ thousand dollars at $x = 2$ thousand units

Question 3

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x - 4)(x - 5)$

Question 4

If $f(x) = 3x - 7$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$5$

Question 5

A ball is thrown upward from the ground with an initial velocity of $32$ ft/s. Its height after $t$ seconds is given by $h(t) = -16t^2 + 32t$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$t = 1$ second

Question 6

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

Accepted Answer

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

Question 7

Solve for $x$: $\log_{2}(x) = 5$.

Accepted Answer

$x = 32$

Question 8

A radioactive substance decays according to $A(t) = 100e^{-0.3t}$, where $A$ is the amount remaining after $t$ years. How much remains after $5$ years (rounded to the nearest whole number)?

Accepted Answer

$22$

Question 9

Which of the following equations represents a line parallel to $y = 3x - 7$?

Accepted Answer

$y = 3x + 2$

Question 10

If $f(x) = x^2 - 4x + 3$, what is the vertex of the parabola?

Accepted Answer

$(2, -1)$

Question 11

A population of bacteria doubles every 3 hours. If the initial population is 500, what is the population after 9 hours?

Accepted Answer

$4000$

Question 12

Which of the following is the solution to the system: $2x + 3y = 7$ and $x - y = 1$?

Accepted Answer

$(2, 1)$

Question 13

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

Accepted Answer

$x 
eq 4$

Question 14

If $f(x) = \sqrt{x-1}$, for which values of $x$ is $f(x)$ defined?

Accepted Answer

$x \geq 1$

Question 15

A car depreciates in value by $15\%$ each year. If the car is worth $20,000$ now, what will it be worth after $2$ years? (Round to the nearest dollar.)

Accepted Answer

$14,450$

Question 16

Which of the following is the solution to $|2x - 5| = 7$?

Accepted Answer

$x = 6$ or $x = -1$

Question 17

Which of the following is the correct solution for $x$ in the equation $\frac{3}{x} = 6$?

Accepted Answer

$x = 0.5$

Question 18

If $f(x) = 2x^2 - 8x + 6$, what is the minimum value of $f(x)$?

Accepted Answer

$-2$

Question 19

A loan of $5000$ is made at an annual interest rate of $6\%$ compounded annually. What is the amount owed after $3$ years? (Round to the nearest dollar.)

Accepted Answer

$5,955$

Question 20

Which of the following is the range of the function $f(x) = x^2 + 4$?

Accepted Answer

$[4, \infty)$

MAT137 Fall 2025 Course Schedule and Chapter Overview

Study Guide - Practice Questions

Study Guide - Flashcards