Q: A function $f$ is increasing on the interval $(2, \infty)$. What does this mean?

For all $x_1 < x_2$ in $(2, \infty)$, $f(x_1) < f(x_2)$

Q: Which of the following best describes the graph of $f(x) = |x|$?

A V-shaped graph opening upwards

Q: A function $f(x)$ is defined as $f(x) = 3x - 2$. What is the slope and what does it represent in a real-world context?

Slope is $3$; it represents the rate of change.

Question 1

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

Accepted Answer

$-2$ miles$/$	ext{second}$

Question 2

Which of the following functions is a constant function?

Accepted Answer

$f(x) = 0x + 5$

Question 3

Given the function $f(x) = -5 + 2x$, what is the $y$-intercept?

Accepted Answer

$-5$

Question 4

Find the slope of the line passing through the points $(2,1)$ and $(5,-4)$.

Accepted Answer

$-5/3$

Question 5

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 6

A function $f(x)$ is defined as $f(x) = x^2 + 1$. Is this function linear or nonlinear?

Accepted Answer

Nonlinear, because the rate of change is not constant.

Question 7

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

Accepted Answer

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

Question 8

Which of the following best describes the graph of $f(x) = 3$?

Accepted Answer

A horizontal line

Question 9

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

Accepted Answer

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

Question 10

A function $f$ is increasing on the interval $(2, \infty)$. What does this mean?

Accepted Answer

For all $x_1 < x_2$ in $(2, \infty)$, $f(x_1) < f(x_2)$

Question 11

Which of the following is NOT a function?

Accepted Answer

A vertical line $x = 2$

Question 12

If a function $f(x)$ is decreasing on $(-\infty, -2) \cup (2, \infty)$, which of the following intervals is $f(x)$ NOT decreasing?

Accepted Answer

$(-2, 2)$

Question 13

Given the function $f(x) = 2x - 4$, what is the $x$-intercept?

Accepted Answer

$(2, 0)$

Question 14

Which of the following best describes the graph of $f(x) = |x|$?

Accepted Answer

A V-shaped graph opening upwards

Question 15

Suppose $A(x) = 100 \left[1 - \frac{x}{5}\right]$ gives the amount of water in a tank after $x$ minutes. What is the average rate of change of $A$ from $x=1$ to $x=1.5$?

Accepted Answer

$-20$ gallons per minute

Question 16

Which of the following statements about the function $f(x) = x^2$ is true?

Accepted Answer

Its range is $[0, \infty)$

Question 17

If the slope $m$ of a linear function is zero, what does its graph look like?

Accepted Answer

A horizontal line

Question 18

Which of the following is an example of a nonlinear function?

Accepted Answer

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

Question 19

A function $f(x)$ is defined as $f(x) = 3x - 2$. What is the slope and what does it represent in a real-world context?

Accepted Answer

Slope is $3$; it represents the rate of change.

Linear and Nonlinear Functions: Key Concepts in College Algebra

Study Guide - Practice Questions

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