Chapter 1.2, Problem 53E

To determine

To find:The graph of the given equation.

Answer to Problem 53E

The graph of the given equation is shown in Figure-1.

Explanation of Solution

Given information:

Theequation is $y=\left|x-6\right|$ .

Calculation:

Consider the equation.

  $y=\left|x-6\right|$

The $x$ intercept is,

  $\begin{array}{l}0=\left|x-6\right|\\ x=6\end{array}$

The $y$ intercept is,

  $\begin{array}{l}y=\left|0-6\right|\\ y=6\end{array}$

The $x$ intercept is $\left(6,0\right)$ and the $y$ intercept is $\left(0,6\right)$ .

For symmetry about $y$ axis substitute $x=-x$ , then we get $y=\left|-x-6\right|$ .

For symmetry about $x$ axis substitute $y=-y$ , then we get $-y=\left|x-6\right|$ .

For symmetry about the origin substitute $x=-x,y=-y$ , then we get $-y=\left|-x-6\right|$ .

Since, none of the above condition result in the equivalent equation.

Thus, the equation is not symmetric.

The graph is shown below.

  

Figure-1