Chapter 2.2, Problem 18AYU

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 18AYU

Solution:

A function.

a. Domain of the function $=\left\{x|0\le x<4\right\}$; Range of the function $=\left\{y|0\le y<3\right\}$.

Explanation of Solution

Given:

The following graph

Calculation:

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

a. Domain of the function $=\left\{x|0\le x<4\right\}$; Range of the function $=\left\{y|0\le y<3\right\}$.

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 18AYU

Solution:

A function.

b. $x\text{-intercept}$ is $\left(0,0\right)$.

Explanation of Solution

Given:

The following graph

Calculation:

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

b. $x\text{-intercept}$ is $\left(0,0\right)$.

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 18AYU

Solution:

A function.

c. No symmetry.

Explanation of Solution

Given:

The following graph

Calculation:

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

c. No symmetry.