Chapter 5.8, Problem 11P

Graph each function by translating $y=\left|x\right|$. $y=|x+6|$

To determine

Draw the graph of the function $y=\left|x+6\right|$ by translating $y=\left|x\right|$ .

Answer to Problem 11P

The graph of the equation is:

  

Explanation of Solution

Given information:

The given function is $y=\left|x+6\right|$ .

Calculation:

Consider the equations $y=\left|x+6\right|$ and $y=\left|x\right|$ .

In the equation $y=\left|x\right|$ translating 6 units left then the equation becomes $y=\left|x+6\right|$ .

When drawing the graph, each point of $y=\left|x+6\right|$ , is 6 units left from the corresponding points of $y=\left|x\right|$ .

Thus, the translation occurs 6 units left with $y=\left|x\right|$ .

The graph of the equation is:

  

Hence, a translation occurs 6 units left with $y=\left|x\right|$ .