$\{x \mid x \neq 2, x \neq -2\}$

Question 1

Which of the following relations is a function?

Accepted Answer

The set of ordered pairs $\{(2,5), (3,6), (4,7)\}$

Question 2

What is the domain of the function $f(x) = \frac{1}{x-3}$?

Accepted Answer

$\{x \mid x 
eq 3\}$

Question 3

For the function $f(x) = x^2 - 4x + 3$, on which interval is the function decreasing?

Accepted Answer

$(-\infty, 2)$

Question 4

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3$

Question 5

Calculate the slope of the line passing through the points $(2, 5)$ and $(6, 13)$.

Accepted Answer

$2$

Question 6

What is the equation of the line in point-slope form passing through $(1, -2)$ with slope $m = 3$?

Accepted Answer

$y + 2 = 3(x - 1)$

Question 7

Which of the following lines is perpendicular to $y = 2x + 5$?

Accepted Answer

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

Question 8

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

Accepted Answer

$(x + 1)^2$

Question 9

Given $f(x) = \sqrt{x-2}$, what is the domain of $f$?

Accepted Answer

$\{x \mid x \geq 2\}$

Question 10

If $f(x) = 2x + 1$ and $g(x) = x^2$, write $h(x) = f(g(x))$ as a composition.

Accepted Answer

$h(x) = 2x^2 + 1$

Question 11

Which pair of functions are inverses of each other?

Accepted Answer

$f(x) = 2x + 3$ and $g(x) = \frac{x - 3}{2}$

Question 12

Find the inverse of the function $f(x) = 5x - 7$.

Accepted Answer

$f^{-1}(x) = \frac{x + 7}{5}$

Question 13

What is the distance between the points $(3, 4)$ and $(7, 1)$?

Accepted Answer

$5$

Question 14

A function $f(x)$ is even if:

Accepted Answer

$f(-x) = f(x)$

Question 15

Which transformation represents a vertical shift up by 3 units for $f(x)$?

Accepted Answer

$f(x) + 3$

Question 16

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

Accepted Answer

$4x^2$

Question 17

Which of the following equations represents a function?

Accepted Answer

$y = x^3 + 2$

Question 18

Given the function $f(x) = \frac{1}{x^2 - 4}$, what is its domain?

Accepted Answer

$\{x \mid x 
eq 2, x 
eq -2\}$

Question 19

If $f(x) = x^2$ and $g(x) = \sqrt{x}$, what is $f(g(x))$?

Accepted Answer

$x$

College Algebra Exam Question Topics – Step-by-Step Study Guidance

Study Guide - Practice Questions