Chapter 1.3, Problem 30E

Solution

To graph: The of a function and find its domain.

Given information:

The function is $g\left(x\right)=\left|x-4\right|$ .

Graph:

The graph of the function $g\left(x\right)=\left|x-4\right|$ is shown in Fig.1.

  

The domain of a function is the set in which the function is defined.

From the Fig. (1), it is clear that when $x\to -\infty \text{and}x\to +\infty$ the function $g\left(x\right)\to \infty$ that shows, the function $g\left(x\right)=\left|x-4\right|$ is defined in the interval $\left(-\infty ,\infty \right)$ .

Therefore, the domain the function $g\left(x\right)=\left|x-4\right|$ is $\left(-\infty ,\infty \right)$ .

Interpretation:

The graph of the function $g\left(x\right)=\left|x-4\right|$ is a triangle with one vertex at $\left(4,0\right)$ whose third side exists at infinity.