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 $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

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 $$2^{x}$$ \u003e 16$$?

Accepted Answer

$$x \u003e 4$$

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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