Question 1

Which of the following functions is symmetric with respect to the y-axis?

Accepted Answer

$f(x) = x^2 + 4$

Question 2

Given the function $f(x) = \sqrt{x-3}$, which of the following describes its domain?

Accepted Answer

$x \geq 3$

Question 3

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

Accepted Answer

$C(x) = 225 + 6.75x$

Question 4

Which of the following is the equation of a circle with center at $(2, 7)$ and radius $8$?

Accepted Answer

$(x-2)^2 + (y-7)^2 = 64$

Question 5

Solve for $x$: $3x^2 + 4x = 19$

Question 6

Given $f(x) = 2x + 3$ and $g(x) = \dfrac{1}{x^2 - 4x + 5}$, what is the domain of $g(x)$?

Accepted Answer

$x \in \mathbb{R}$

Question 7

Which of the following describes the transformation from $f(x) = x$ to $g(x) = \sqrt{x-3} - 2$?

Accepted Answer

Shift right 3 units, down 2 units, and change to a square root function

Question 8

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 9

Solve the system of equations: $\begin{cases} 2x + y = 5 \ 3x - y = 4 \end{cases}$

Accepted Answer

$x = 2, y = 1$

Question 10

Which of the following best describes the range of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$[0, \infty)$

Question 11

If $f(x) = x^2 - 4x + 3$, what are the $x$-intercepts of the graph?

Accepted Answer

$x = 1$ and $x = 3$

Question 12

Which of the following is the inverse of $f(x) = 2x + 3$?

Accepted Answer

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

Question 13

Solve the inequality $2x - 3 > 7$. Write the solution in interval notation.

Accepted Answer

$(5, \infty)$

Question 14

Which of the following best describes the end behavior of $f(x) = -x^3 + 2x$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o -\infty$

Question 15

Which of the following is the solution to $\dfrac{2x-1}{x+3} = 1$?

Accepted Answer

$x = 4$

Question 16

A line passes through the point $(-5,2)$ and is parallel to the line $y = 3x - 5$. What is its equation?

Accepted Answer

$y = 3x + 17$

Question 17

Which of the following is the correct solution to $3x^2 - 5x - 2 = 0$?

Accepted Answer

$x = 2, x = -\dfrac{1}{3}$

Question 18

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

Accepted Answer

$(2, -1)$

Question 19

Which of the following is the solution to the system of inequalities $\begin{cases} x - 2y \leq 10 \ 3x - 4y > 8 \end{cases}$?

Accepted Answer

$x = 6, y = -2$

Question 20

If $f(x) = x^2 - 4x + 3$, for which value of $x$ does $f(x)$ attain its minimum?

Accepted Answer

$x = 2$

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards