Question 1

Which of the following equations represents a linear function with a slope of $-3$ and a $y$-intercept of $5$?

Accepted Answer

$f(x) = -3x + 5$

Question 2

Given the points $(2, 1)$ and $(3, -4)$, what is the slope $m$ of the line passing through them?

Accepted Answer

$m = \frac{-4 - 1}{3 - 2} = \frac{-5}{1} = -5$

Question 3

A function $f(x)$ is called a constant function if:

Accepted Answer

Its slope $m$ is $0$ and its graph is a horizontal line.

Question 4

Which of the following is NOT a function?

Accepted Answer

A vertical line $x = 2$.

Question 5

Find the $x$-intercept of the line $f(x) = 2x - 4$.

Accepted Answer

$(2, 0)$

Question 6

Which of the following functions is nonlinear?

Accepted Answer

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

Question 7

Given the function $f(x) = x^2$, what is its domain and range?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[0, \infty)$

Question 8

For the function $f(x) = \sqrt{x}$, which of the following best describes its domain and range?

Accepted Answer

Domain: $[0, \infty)$, Range: $[0, \infty)$

Question 9

Which interval describes where the function $f(x)$ is increasing if $f(x)$ is shown to rise from left to right between $x = -2$ and $x = 2$?

Accepted Answer

$(-2, 2)$

Question 10

A car's speed is $30$ mph at $t = 2$ seconds and $24$ mph at $t = 5$ seconds. What is the average rate of change of the speed from $t = 2$ to $t = 5$ seconds?

Accepted Answer

$-2$ mph$/$sec$

Question 11

Given $f(x) = |x|$, what is the range of $f$?

Accepted Answer

$[0, \infty)$

Question 12

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

Accepted Answer

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

Question 13

Suppose a function $g(x)$ is decreasing on the interval $(-\infty, -2) \cup (2, \infty)$. Which of the following is true?

Accepted Answer

The function is decreasing for $x < -2$ and $x > 2$.

Question 14

If the graph of a function passes the vertical line test, what does this indicate?

Accepted Answer

It is a function.

Question 15

Given the function $f(x) = x^3$, what is its range?

Accepted Answer

$(-\infty, \infty)$

Question 16

Which of the following is the correct formula for the slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Question 17

A tank contains $100$ gallons of water. The amount of water remaining after $x$ minutes is $A(x) = 100 \left(1 - \frac{x}{5}\right)$. What is the average rate of change of $A$ from $x = 1$ to $x = 1.5$?

Accepted Answer

$-20$ gallons/minute

Question 18

Which of the following best describes a function that is increasing on $(2, \infty)$ and decreasing on $(-\infty, 2)$?

Accepted Answer

A function with a maximum at $x = 2$

Question 19

If $f(x) = 2x + 1$ and $g(x) = x^2 + 1$, which function is linear and which is nonlinear?

Accepted Answer

$f(x)$ is linear, $g(x)$ is nonlinear

Linear and Nonlinear Functions: Key Concepts in College Algebra

Study Guide - Practice Questions

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