Chapter 1.2, Problem 21E

To determine

The $x-\text{intercept}$ and $y-\text{intercept}$ of the graph of the equation $y=\left|x+2\right|$ .

  

Answer to Problem 21E

The $x-\text{intercept}$ of the graph is the points $\left(x,y\right)=\left(-2,0\right)$

The $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,2\right)$

Explanation of Solution

Given:

The equation $y=\left|x+2\right|$ with its graph

  

Concept Used:

The $x-\text{intercept}$ is a point on the graph where the graph intersects $x-\text{axis}$ i.e., where the $y$ coordinate is zero.

The $y-\text{intercept}$ is a point on the graph where the graph intersects $y-\text{axis}$ i.e., where the $x$ coordinate is zero.

Calculation:

The equation $y=\left|x+2\right|$ with its graph

  

Since, the graph intersects $x-\text{axis}$ at $\left(x,y\right)=\left(-2,0\right)$ .

Therefore, $x-\text{intercept}$ of the graph is the points $\left(x,y\right)=\left(-2,0\right)$ .

Since, the graph intersects $y-\text{axis}$ at $\left(x,y\right)=\left(0,2\right)$

Therefore, $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,2\right)$