Chapter 2.2, Problem 13AYU

In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:

(a) The domain and range

(b) The intercepts, if any

(c) Any symmetry with respect to the $x\text{-axis}$, the $y\text{-axis}$, or the origin

To determine

To find: The given graph is that of a function by using vertical-line test; if it is, using the graph to find.

a. The domain and range;

Answer to Problem 13AYU

Solution:

A function;

a. Domain of the function $=\left\{x\right|-\pi \le x\le \pi \}$; Range $=\left\{y\right|-1\le y\le 1\}$.

Explanation of Solution

Given:

The following graph

Calculation:

The given graph is a graph of a function because every vertical line interests the graph in at most one point.

a. Domain of the function $=\left\{x\right|-\pi \le x\le \pi \}$; Range $=\left\{y\right|-1\le y\le 1\}$.

To determine

To find: The given graph is that of a function by using vertical-line test; if it is, using the graph to find.

b. The intercepts, if any;

Answer to Problem 13AYU

Solution:

A function;

b. $y\text{-intercept}$ is $\left(0,1\right)$; $x\text{-intercept}$ - $(- \frac{\pi }{2},0),(\frac{\pi }{2},0)$.

Explanation of Solution

Given:

The following graph

Calculation:

The given graph is a graph of a function because every vertical line interests the graph in at most one point.

b. $y\text{-intercept}$ is $\left(0,1\right)$; $x\text{-intercept}$ - $(- \frac{\pi }{2},0),(\frac{\pi }{2},0)$.

To determine

To find: The given graph is that of a function by using vertical-line test; if it is, using the graph to find.

c. Any symmetry with respect to the $x\text{-axis}$, the $y\text{-axis}$ or the origin.

Answer to Problem 13AYU

Solution:

A function;

c. $f(-\pi )=-1;f(\pi )=-1;$ This implies the function is symmetric with respect to $y\text{-axis}$.

Explanation of Solution

Given:

The following graph

Calculation:

The given graph is a graph of a function because every vertical line interests the graph in at most one point.

c. $f(-\pi )=-1;f(\pi )=-1;$ This implies the function is symmetric with respect to $y\text{-axis}$.