Question 1

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

Accepted Answer

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

Question 2

Given the function $f(x) = 2x + 3$, what is $f^{-1}(x)$, the inverse function?

Accepted Answer

$ f^{-1}(x) = \frac{x - 3}{2} $

Question 3

A company charges a set-up fee of $225, then $6.75$ per shirt to produce new t-shirts. Which function $C(x)$ models the total cost of producing $x$ shirts?

Accepted Answer

$ C(x) = 225 + 6.75x $

Question 4

Which of the following best describes the transformation from $y = \sqrt{x}$ to $y = -2\sqrt{x - 3} + 1$?

Accepted Answer

Shift right 3 units, reflect over the $x$-axis, vertically stretch by 2, shift up 1 unit

Question 5

Solve for $x$: $3x^2 - 4x - 5 = 0$

Accepted Answer

$ x = \frac{4 \pm \sqrt{16 + 60}}{6} $

Question 6

Which of the following is the domain of the function $f(x) = \frac{1}{x^2 - 4x + 3}$?

Accepted Answer

$ (-\infty, 1) \cup (1, 3) \cup (3, \infty) $

Question 7

A population of 7,500 people is experiencing exponential growth at a rate of 2.5% per year. Which equation models the population $P$ after $t$ years?

Accepted Answer

$ P = 7500(1.025)^t $

Question 8

Which of the following best describes the symmetry of the graph of $y = x^2$?

Accepted Answer

Symmetric with respect to the $y$-axis

Question 9

Solve the system of equations: $\begin{cases} 2x + y = 5 \ x - y = 1 \end{cases}$

Accepted Answer

$ x = 2,\ y = 1 $

Question 10

Given $f(x) = x^2 - 4x + 3$, which of the following is a $y$-intercept of the graph?

Accepted Answer

$ (0, 3) $

Question 11

Which of the following is the solution to the inequality $2x - 3 > 7$?

Accepted Answer

$ x > 5 $

Question 12

If $f(x) = x^2 - 6x + 8$, what are the $x$-intercepts of the graph?

Accepted Answer

$ x = 2,\ x = 4 $

Question 13

Which of the following is the equation of a line parallel to $y = 3x + 5$ and passing through the point $(4, -2)$?

Accepted Answer

$ y = 3x - 14 $

Question 14

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

Accepted Answer

$ (2, -1) $

Question 15

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

Accepted Answer

$ x = 8 $

Question 16

Which of the following is the solution to the equation $|2x - 5| = 9$?

Accepted Answer

$ x = 7,\ x = -2 $

Question 17

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

Accepted Answer

$ [0, \infty) $

Question 18

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

Accepted Answer

$ 9 $

Question 19

Which of the following is the solution set for the inequality $x^2 - 9 < 0$?

Accepted Answer

$ (-3, 3) $

Question 20

Which of the following is the factored form of $x^2 - 5x + 6$?

Accepted Answer

$ (x - 2)(x - 3) $

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards