Question 1

Which of the following best describes the domain of a function $f(x)$?

Accepted Answer

The set of all possible $x$-values for which $f(x)$ is defined.

Question 2

Given the points $A(2, 3)$ and $B(5, 7)$, what is the distance between them?

Accepted Answer

$\sqrt{(5-2)^2 + (7-3)^2}$

Question 3

Which of the following is the correct midpoint formula for points $A(x_1, y_1)$ and $B(x_2, y_2)$?

Accepted Answer

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Question 4

If a function $f(x)$ has a denominator, which values must be excluded from the domain?

Accepted Answer

Values that make the denominator zero.

Question 5

What is the slope of the line passing through the points $(1, 2)$ and $(4, 8)$?

Accepted Answer

$\frac{8-2}{4-1}$

Question 6

Which of the following is the general point-slope form of a line?

Accepted Answer

$y - y_1 = m(x - x_1)$

Question 7

If a line has a slope of $m = 0$, what can you say about the line?

Accepted Answer

It is a horizontal line.

Question 8

Which of the following is the correct way to write the equation of a line in slope-intercept form?

Accepted Answer

$y = mx + b$

Question 9

If a function passes the vertical line test, what does this mean?

Accepted Answer

Each $x$-value has only one $y$-value.

Question 10

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

Accepted Answer

All real numbers except $x = 2$

Question 11

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible $y$-values for which $f(x)$ is defined.

Question 12

If you are given the equation $y = 3x + 2$, what is the $y$-intercept?

Accepted Answer

$2$

Question 13

Which of the following is true about the slopes of parallel lines?

Accepted Answer

They are equal.

Question 14

If a line has the equation $x = 5$, what type of line is this?

Accepted Answer

A vertical line.

Question 15

Which of the following is the correct formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Question 16

A real-world application: A chemist needs to mix two solutions. The concentration of solution A is $x$ and solution B is $y$. If the total concentration must be $10$, which equation represents this scenario?

Accepted Answer

$x + y = 10$

Question 17

If the graph of a function opens upwards and passes through the origin, which of the following could be its equation?

Accepted Answer

$y = x^2$

Question 18

If a function $f(x)$ is defined as $f(x) = \frac{1}{x}$, which value must be excluded from the domain?

Accepted Answer

$x = 0$

Question 19

Which of the following is the correct way to find the $x$-intercept of a function $f(x)$?

Accepted Answer

Set $f(x) = 0$ and solve for $x$.

College Algebra Quiz 2 Review – Functions, Graphs, and Linear Equations

Study Guide - Practice Questions

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