Symmetric with respect to the $y$-axis

Slope: $-2$, $y$-intercept: $5$

Question 1

Solve the inequality $2x - 5 \leq 7$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 6]$

Question 2

Which of the following graphs represents the solution set to $x > -2$?

Accepted Answer

A number line with an open circle at $-2$ and shading to the right

Question 3

Solve the compound inequality $-1 < 2x + 3 \leq 7$ and express the solution in interval notation.

Accepted Answer

$(-2, 2]$

Question 4

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

Accepted Answer

$-1$

Question 5

Which of the following equations defines $y$ as a function of $x$?

Accepted Answer

$y = \sqrt{x}$

Question 6

Use the vertical line test to determine if the graph of a circle centered at the origin is a function of $x$. Which statement is correct?

Accepted Answer

It is not a function of $x$

Question 7

Find the slope of the line passing through the points $(2, 3)$ and $(5, 11)$.

Question 8

Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ 2x-1 & x \geq 0 \end{cases}$, what is $f(-3)$?

Accepted Answer

$-1$

Question 9

Determine whether the function $f(x) = x^3$ is even, odd, or neither.

Accepted Answer

Odd

Question 10

A function $f$ is increasing on the interval $(-\infty, 2)$ and decreasing on $(2, \infty)$. What is the nature of $x=2$?

Accepted Answer

Relative maximum

Question 11

Solve the inequality $|2x - 3| < 5$ and express the solution in interval notation.

Accepted Answer

$(-1, 4)$

Question 12

Which of the following best describes the symmetry of the graph of $f(x) = x^4$?

Accepted Answer

Symmetric with respect to the $y$-axis

Question 13

Given the function $f(x) = 2x^2 - 8x + 6$, find the vertex of the parabola.

Accepted Answer

$(2, -2)$

Question 14

Find the $y$-intercept of the line with equation $3x - 2y = 6$.

Accepted Answer

$(0, -3)$

Question 15

A company charges $f(w) = 0.5w + 0.25$ dollars to mail a letter weighing $w$ ounces. What is the cost to mail a letter that weighs $3$ ounces?

Accepted Answer

$1.25$

Question 16

Which of the following intervals describes where the function $f(x)$ is constant if $f(x)$ is a horizontal line?

Accepted Answer

$(-\infty, \infty)$

Question 17

Given the equation $y = -2x + 5$, what is the slope and $y$-intercept?

Accepted Answer

Slope: $-2$, $y$-intercept: $5$

Question 18

If $f(x) = x^2 - 4$ and $g(x) = 2x + 1$, what is $(f + g)(3)$?

Accepted Answer

$10$

Question 19

Which of the following is the equation of the line passing through $(0, 2)$ with slope $-3$?

Accepted Answer

$y = -3x + 2$

Question 20

Determine the domain of the function $f(x) = \sqrt{x - 1}$.

Accepted Answer

$[1, \infty)$

College Algebra Study Guide: Equations, Inequalities, Functions, and Graphs

Study Guide - Practice Questions