A graph where every vertical line intersects the graph at most once.

Domain: all real $x$, Range: $y \geq k$ for some $k$

The graph of $g$ is the graph of $f$ shifted down.

Question 1

Which of the following sets represents the domain of the relation $\{(1,2), (2,5), (5,7), (7,0)\}$?

Accepted Answer

$\{1, 2, 5, 7\}$

Question 2

Given the relation $\{(3,1), (-5,0), (10,-2), (7,1)\}$, what is the range?

Accepted Answer

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

Question 3

Which of the following diagrams represents a function?

Accepted Answer

A mapping where each input is connected to exactly one output.

Question 4

Given $f(x) = x^2 + 4x + 10$, what is $f(-2)$?

Accepted Answer

$6$

Question 5

Which of the following equations does NOT represent a function?

Accepted Answer

$y = \pm \sqrt{x + 13}$

Question 6

What is the interval notation for the set $\{x \mid 2 \leq x < 7\}$?

Accepted Answer

$[2, 7)$

Question 7

Which graph passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line intersects the graph at most once.

Question 8

Given the graph of $f(x)$ is a parabola opening upwards, what is the domain and range?

Accepted Answer

Domain: all real $x$, Range: $y \geq k$ for some $k$

Question 9

If a function $f(x)$ is even, which of the following must be true?

Accepted Answer

$f(-x) = f(x)$ for all $x$

Question 10

What is the slope of the line passing through the points $(3,4)$ and $(6,7)$?

Accepted Answer

$1$

Question 11

Which of the following lines is perpendicular to the line $y = 2x + 1$?

Accepted Answer

$y = -\frac{1}{2}x + 3$

Question 12

Given $f(x) = 3x - 2$ and $g(x) = 3x - 2 - 2$, how is the graph of $g$ related to $f$?

Accepted Answer

The graph of $g$ is the graph of $f$ shifted down.

Question 13

For the piecewise function $f(x) = \begin{cases} 2x+5 & x < 2 \ x^2+7 & x \geq 2 \end{cases}$, what is $f(3)$?

Accepted Answer

$16$

Question 14

What is the difference quotient for $f(x) = 3x + 7$?

Accepted Answer

$3$

Question 15

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(x)$?

Accepted Answer

$(x+1)^2$

Question 16

Which of the following is the inverse of $f(x) = 3x - 5$?

Accepted Answer

$f^{-1}(x) = \frac{x+5}{3}$

Question 17

Given the function $f(x) = \sqrt{x-7}$, what is its domain?

Accepted Answer

$[7, \infty)$

Question 18

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

Accepted Answer

$(x-1)^2 - 2(x-1) + 1$

Question 19

Which of the following best describes the average rate of change of a function $f(x)$ from $x=a$ to $x=b$?

Accepted Answer

$\frac{f(b) - f(a)}{b - a}$

Question 20

If two lines are perpendicular and the slope of one is $m$, what is the slope of the other?

Accepted Answer

$-\frac{1}{m}$

College Algebra: Functions, Graphs, and Linear Equations Study Notes

Study Guide - Practice Questions