Q: Which of the following is the domain of the function $f(x) = \sqrt{3x + 4}$?

$\left[ -\frac{4}{3}, \infty \right)$

Q: Which of the following graphs represents a relation that is NOT a function?

A circle centered at the origin.

Q: Which of the following is the correct interval notation for all real numbers except $x = 2$?

$(-\infty, 2) \cup (2, \infty)$

Question 1

Which of the following best describes the relation shown in the table where time (in seconds) is paired with height (in meters) for a rock thrown on the Moon?

Accepted Answer

A function, because each time value corresponds to exactly one height value.

Question 2

Given the relation $\{(0, 3), (-1, 4), (0, 5), (3, 0)\}$, what is the domain and range?

Accepted Answer

Domain: $\{0, -1, 3\}$, Range: $\{3, 4, 5, 0\}$

Question 3

Which of the following equations does NOT represent a function?

Accepted Answer

$x^2 + y^2 = 1$

Question 4

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

Accepted Answer

$4$

Question 5

What is the domain of the function $f(x) = \sqrt{x - 5}$?

Accepted Answer

$[5, \infty)$

Question 6

For the function $f(x) = \frac{x+3}{x+4}$, what value(s) must be excluded from the domain?

Accepted Answer

$x = -4$

Question 7

If $f(x) = |x| + 5$, which transformation has been applied to the parent function $f(x) = |x|$?

Accepted Answer

A vertical shift up by 5 units.

Question 8

Which of the following is the parent function for $g(x) = 2x^2 - 1$?

Accepted Answer

$f(x) = x^2$

Question 9

Given the graph of $y = x^2$, which transformation results in the graph of $y = x^2 - 4$?

Accepted Answer

A vertical shift down by 4 units.

Question 10

Suppose a function $f(x)$ is positive for $x$ in the interval $(1, 4)$ and negative for $x$ in the interval $(-2, 1)$. Which statement is true?

Accepted Answer

$f(x) > 0$ for $1 < x < 4$

Question 11

Which of the following describes a vertical stretch of the parent function $f(x) = \sqrt{x}$ by a factor of 2?

Accepted Answer

$f(x) = 2\sqrt{x}$

Question 12

If $f(x) = x^2$, what is the effect of the transformation $f(-x)$ on the graph?

Accepted Answer

Reflection over the y-axis.

Question 13

Given the function $f(x) = \frac{x}{x-2}$, what is the y-intercept?

Accepted Answer

$(0, 0)$

Question 14

Which of the following is the domain of the function $f(x) = \sqrt{3x + 4}$?

Accepted Answer

$\left[ -\frac{4}{3}, \infty \right)$

Question 15

Which of the following graphs represents a relation that is NOT a function?

Accepted Answer

A circle centered at the origin.

Question 16

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

Accepted Answer

$16x^2$

Question 17

Which of the following is the correct interval notation for all real numbers except $x = 2$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 18

Given the function $f(x) = \frac{x+2}{x-1}$, for which value of $x$ is the function undefined?

Accepted Answer

$x = 1$

Question 19

Which transformation will reflect the graph of $f(x)$ over the x-axis?

Accepted Answer

$y = -f(x)$

College Algebra Study Guide: Functions and Their Graphs

Study Guide - Practice Questions

Study Guide - Flashcards