Question 1

Which of the following intervals represents the solution set to the inequality $x^3 - 3x^2 + 2x \geq 0$?

Accepted Answer

$[0,1] \cup [2, \infty)$

Question 2

Given the equation $\frac{2x}{x-2} + 3 = \frac{4}{x-2}$, what is the solution set?

Accepted Answer

No solution

Question 3

Which of the following is the correct set-builder notation for the interval $(-\infty, 1) \cup (4, \infty)$?

Accepted Answer

$\{x \mid x < 1 	ext{ or } x > 4\}$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$\{(1,2), (1,3), (2,4)\}$

Question 5

What is the domain of the function $f(x) = \frac{1}{x+1}$?

Accepted Answer

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

Question 6

Given the quadratic equation $6x^2 - 17x + 12 = 0$, what are its solutions?

Accepted Answer

$x = \frac{3}{2}, \frac{4}{3}$

Question 7

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 8

If $y = x^2 - 4x + 4$, what is the vertex of the parabola?

Accepted Answer

$(2, 0)$

Question 9

Which of the following describes the range of the function $f(x) = x^2 - 4x + 4$?

Accepted Answer

$[0, \infty)$

Question 10

Given the relation $\{(0,7), (1,5), (2,7), (3,6)\}$, what is the domain?

Accepted Answer

$\{0,1,2,3\}$

Question 11

Which of the following equations does NOT represent $y$ as a function of $x$?

Accepted Answer

$x^2 + y^2 = 16$

Question 12

What is the solution set to the inequality $x-4 < 0$?

Accepted Answer

$(-\infty, 4)$

Question 13

If $f(x) = \frac{1}{x-2}$, which value is NOT in the domain of $f$?

Accepted Answer

$x = 2$

Question 14

Which of the following best describes the range of the relation $\{(a, e), (b, f), (c, g), (d, f)\}$?

Accepted Answer

$\{e, f, g\}$

Question 15

Which of the following is the correct interval notation for the set $\{x \mid x \leq -1 	ext{ or } x > 4\}$?

Accepted Answer

$(-\infty, -1] \cup (4, \infty)$

Question 16

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

Accepted Answer

$1$

Question 17

Which of the following is the correct definition of a relation?

Accepted Answer

A correspondence between two sets such that each element of the first set is paired with one or more elements of the second set.

Question 18

Given the function $f(x) = \frac{1}{x^2 - 9}$, what is the domain?

Accepted Answer

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

Question 19

If a relation has domain $\{a, b, c, d\}$ and range $\{e, f, g\}$, which of the following could be a function?

Accepted Answer

$\{(a,e), (b,f), (c,g), (d,f)\}$

Foundations of Relations, Functions, and Equations in College Algebra

Study Guide - Practice Questions