Chapter 2.2, Problem 20AYU

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;

b. The intercepts, if any;

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

Answer to Problem 20AYU

Solution:

A function

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

b. $x\text{-intercepts}$ are $\left(-3,0\right),\left(2,0\right),\left(0,2\right)$.

c. 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 that interests the graph in at most one point.

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

b. $x\text{-intercepts}$ are $\left(-3,0\right),\left(2,0\right),\left(0,2\right)$.

c. No symmetry.