Substitute $-x$ for $x$ and $-y$ for $y$ in the equation and check if you get the original equation.

It is used to find the rate of change or slope of a function.

Question 1

Which of the following best describes the behavior of the function shown in the first image (blue line going up from left to right)?

Accepted Answer

The function is increasing on its entire domain.

Question 2

For the function shown in the second image (blue line going down from left to right), what is the interval of increase?

Accepted Answer

The function is not increasing on any interval.

Question 3

The function in the third image (horizontal blue line) is best described as:

Accepted Answer

Constant everywhere.

Question 4

Which of the following statements about the function in the fourth image (red parabola opening upward) is correct?

Accepted Answer

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

Question 5

A function $f(x)$ is said to be even if:

Accepted Answer

$f(-x) = f(x)$ for all $x$ in the domain.

Question 6

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3 - 2x$

Question 7

If a function is symmetric with respect to the y-axis, which of the following must be true?

Accepted Answer

For every point $(x, y)$, the point $(-x, y)$ is also on the graph.

Question 8

Consider the piecewise function $f(x) = \begin{cases} x + 2 & 	ext{if } x \leq 1 \ 4 & 	ext{if } x > 1 \end{cases}$. What is $f(0)$?

Accepted Answer

$f(0) = 0 + 2 = 2$

Question 9

Given $f(x) = 2x^2 - x + 3$, what is the simplified difference quotient $\frac{f(x+h) - f(x)}{h}$?

Accepted Answer

$4x + 2h - 1$

Question 10

Which of the following is true about the function $f(x) = x^2 + 2x + 1$?

Accepted Answer

It is neither even nor odd.

Question 11

A function $f(x)$ is decreasing on an interval if:

Accepted Answer

The y-values get smaller as the x-values get larger.

Question 12

Which of the following is a real-world example of a piecewise function?

Accepted Answer

A cell phone plan charges $\$0.10$ per minute for the first 100 minutes and $\$0.05$ per minute after that.

Question 13

If $f(x) = x^2 - 6x$, is $f(x)$ even, odd, or neither?

Accepted Answer

Neither

Question 14

Which of the following is the correct definition of a relative minimum?

Accepted Answer

A function value $f(b)$ is a relative minimum if $f(b) < f(x)$ for all $x$ not equal to $b$ in an open interval containing $b$.

Question 15

Which test would you use to determine if a function is symmetric with respect to the origin?

Accepted Answer

Substitute $-x$ for $x$ and $-y$ for $y$ in the equation and check if you get the original equation.

Question 16

If $f(x) = 3x + 5$ for $x < 0$ and $f(x) = 4x + 7$ for $x \geq 0$, what is $f(-1)$?

Accepted Answer

$f(-1) = 3(-1) + 5 = 2$

Question 17

Which of the following statements is true about the difference quotient?

Accepted Answer

It is used to find the rate of change or slope of a function.

Question 18

If a function $f(x)$ is constant on an interval, what does this mean about its graph?

Accepted Answer

The graph is a horizontal line on that interval.

Question 19

Which of the following functions is neither even nor odd?

Accepted Answer

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

Section 2.2: More on Functions and Their Graphs – College Algebra Study Notes

Study Guide - Practice Questions