No, $y$ is not a function of $x$.

Question 1

Which of the following values is NOT in the domain of the function $f(x) = \frac{2}{x+3} - \frac{1}{x-2}$?

Accepted Answer

$x = -3$

Question 2

Given the equation $\frac{4}{x+10} + \frac{1}{x+2} = \frac{5x+1}{(x+10)(x+2)}$, what is the equation after clearing the denominators?

Accepted Answer

$4(x+2) + 1(x+10) = 5x+1$

Question 3

Solve for $x$: $8x\left(\frac{2}{x}\right) + 3x(1) = \frac{3}{4x} + 8x\left(\frac{15}{8x}\right)$

Accepted Answer

$x = \frac{10}{7}$

Question 4

What values make the denominator zero in the rational expression $\frac{6x}{x+2}$?

Accepted Answer

$x = -2$

Question 5

Solve for $x$: $4x = 3x + 4 - \frac{4}{x+2}$

Accepted Answer

$x = \frac{2}{3}$

Question 6

Use factoring to solve: $x^2 - 6x - 10 = 0$

Question 7

Solve by factoring: $x^2 - 7x - 10 = 0$

Accepted Answer

$x = -5, x = 2$

Question 8

Express the solution to $-6x \leq 18$ in interval notation.

Accepted Answer

$[-3, \infty)$

Question 9

Solve the absolute value inequality $|2x-1| < 3$ and express the solution in interval notation.

Accepted Answer

$(-1, 2)$

Question 10

Solve the absolute value equation $|5x-2| = 13$. What is the solution set?

Accepted Answer

$\{3, -\frac{11}{5}\}$

Question 11

Given the relation $\{(3,2), (4,-1), (5,8)\}$, is this a function? What is the domain?

Accepted Answer

Yes; Domain: $\{3,4,5\}$

Question 12

Given the relation $\{(-2,3), (3,-1), (-2,2), (3,4)\}$, is this a function? What is the range?

Accepted Answer

No; Range: $\{-1,2,3,4\}$

Question 13

Use the vertical line test to determine if $y$ is a function of $x$ for the graph of a circle centered at the origin.

Accepted Answer

No, $y$ is not a function of $x$.

Question 14

What is the $y$-intercept of the function $f(x) = 2x + 3$?

Accepted Answer

$3$

Question 15

If $f(x) = 2x + 3$, what is $f(4)$?

Accepted Answer

$11$

Question 16

Express the solution to $2x + 2x - 2 \leq 8$ in interval notation.

Accepted Answer

$[-3, 5]$

Question 17

What is the domain of the function $f(x) = x^2$?

Accepted Answer

$(-\infty, \infty)$

Question 18

Which of the following intervals represents all $x$ such that $x \geq 7$?

Accepted Answer

$[7, \infty)$

Question 19

If $f(x) = x^2 - 11x + 10$, what are the solutions to $f(x) = 0$?

Accepted Answer

$x = 10, x = 1$

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

Study Guide - Practice Questions