Q: Which of the following best describes the solution set of the quadratic equation $ax^2 + bx + c = 0$ when $b^2 - 4ac < 0$?

Two complex conjugate solutions

Q: A company models its profit $P$ (in thousands of dollars) as a function of the number of units sold $x$ by $P(x) = -2x^2 + 40x - 100$. What is the maximum profit, and how many units should be sold to achieve it?

Maximum profit is $300$ at $x = 10$

Q: If $f(x) = 2x^2 - 3x + 5$ and $g(x) = x - 4$, what is $(f \circ g)(2)$?

$f(g(2)) = 2(-2)^2 - 3(-2) + 5 = 8 + 6 + 5 = 19$

Q: Given the exponential function modeling radioactive decay $N(t) = N_0 e^{-kt}$, which of the following statements is true?

The quantity decreases as $t$ increases

Question 1

Which of the following best describes the solution set of the quadratic equation $ax^2 + bx + c = 0$ when $b^2 - 4ac < 0$?

Accepted Answer

Two complex conjugate solutions

Question 2

A company models its profit $P$ (in thousands of dollars) as a function of the number of units sold $x$ by $P(x) = -2x^2 + 40x - 100$. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $300$ at $x = 10$

Question 3

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 1$

Question 4

If $f(x) = 2x^2 - 3x + 5$ and $g(x) = x - 4$, what is $(f \circ g)(2)$?

Accepted Answer

$f(g(2)) = 2(-2)^2 - 3(-2) + 5 = 8 + 6 + 5 = 19$

Question 5

A cell phone plan charges a base fee of $\$20$ per month plus $\$0.10$ per text message sent. Which function models the total monthly cost $C$ for $x$ text messages?

Accepted Answer

$C(x) = 20 + 0.10x$

Question 6

Which of the following is the correct domain for the function $f(x) = \frac{1}{x-3}$?

Accepted Answer

$x 
eq 3$

Question 7

Given the exponential function modeling radioactive decay $N(t) = N_0 e^{-kt}$, which of the following statements is true?

Accepted Answer

The quantity decreases as $t$ increases

Question 8

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

Accepted Answer

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

Question 9

A ball is thrown upward with an initial velocity of $32$ ft/s from a height of $48$ ft. Its height after $t$ seconds is given by $h(t) = -16t^2 + 32t + 48$. When does the ball reach its maximum height?

Accepted Answer

$t = 1$ second

Question 10

Which of the following best describes the range of the function $f(x) = x^2 - 4x + 7$?

Accepted Answer

$y \geq 3$

Question 11

If $\log_2(x) = 5$, what is the value of $x$?

Accepted Answer

$x = 32$

Question 12

Which of the following equations represents a circle with center at $(2, -3)$ and radius $5$?

Accepted Answer

$(x-2)^2 + (y+3)^2 = 25$

Question 13

A population of bacteria doubles every 3 hours. If the initial population is 500, which function models the population after $t$ hours?

Accepted Answer

$P(t) = 500 \cdot 2^{t/3}$

Question 14

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

Accepted Answer

$-1 < x < 6$

Question 15

If $f(x) = \sqrt{x-2}$, what is the domain of $f$?

Accepted Answer

$x \geq 2$

Question 16

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

Accepted Answer

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

Question 17

A car depreciates in value by 15% each year. If the car is worth $\$20,000$ now, what will its value be after 4 years?

Accepted Answer

$20,000 	imes (0.85)^4$

Question 18

Which of the following is the solution to the equation $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 19

If $f(x) = x^2$ and $g(x) = x + 1$, what is $f(g(3))$?

Accepted Answer

$16$

Question 20

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

MAC1105 College Algebra Syllabus and Course Structure Overview

Study Guide - Practice Questions

Study Guide - Flashcards