Q: Which of the following best describes the range of the function $f(x) = \dfrac{1}{x - 2}$?

$(-\infty, 0) \cup (0, \infty)$

Question 1

Which of the following best describes the domain of the function $f(x) = \sqrt{2x - 8}$?

Accepted Answer

$x \geq 4$

Question 2

A company models its profit $P$ (in thousands of dollars) as a function of the number of units sold $x$ by $P(x) = -2x^2 + 40x - 50$. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $150$ thousand dollars at $x = 10$

Question 3

Which of the following equations represents a line parallel to $3x - 4y = 12$ and passing through the point $(2, -1)$?

Accepted Answer

$3x - 4y = 10$

Question 4

Solve the following system of equations for $x$ and $y$:

$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$

Accepted Answer

$x = 2, y = 1$

Question 5

Which of the following is the inverse function of $f(x) = 5x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x + 7}{5}$

Question 6

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

Accepted Answer

$P = 200 	imes 3^{t/4}$

Question 7

Which of the following is the solution set for $|2x - 5| < 7$?

Accepted Answer

$-1 < x < 6$

Question 8

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

Accepted Answer

$(2, -1)$

Question 9

A car depreciates in value by 15\% each year. If the car is currently worth $\$20,000$, what will its value be after 3 years? (Round to the nearest dollar.)

Accepted Answer

$14,493$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

$19$

Question 12

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

Accepted Answer

$x = 32$

Question 13

A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots if:

Accepted Answer

$b^2 - 4ac = 0$

Question 14

Which of the following best describes the range of the function $f(x) = \dfrac{1}{x - 2}$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 15

A student invests $\$1,000$ in an account that earns 6\% annual interest compounded quarterly. What is the value after 2 years? (Round to the nearest dollar.)

Accepted Answer

$1,127$

Question 16

Which of the following is the solution to the inequality $2^{x} > 16$?

Accepted Answer

$x > 4$

Question 17

If $f(x) = \dfrac{x^2 - 9}{x - 3}$ for $x 
eq 3$, what is $f(5)$?

Accepted Answer

$7$

Question 18

Which of the following is the solution to $e^{2x} = 7$?

Accepted Answer

$x = \dfrac{1}{2} \ln 7$

Question 19

A rectangle has a length that is 3 units more than twice its width. If the area is 65 square units, what is the width?

Accepted Answer

$5$

College Algebra (MAC 1105) Syllabus and Course Structure – Fall 2025

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