Chapter 1.1, Problem 41E

To determine

To find: The domain and range of the function and sketch the graph.

Answer to Problem 41E

The solution of the given function is all real values except $x\ne 0$ and the range of the function is $2\text{or}\text{4}$ .

Explanation of Solution

Given information:

The given function is,

  $G\left(x\right)=\frac{3x+\left|x\right|}{x}$

The domain of the function is,

  $x\ne 0$

The range of the function is calculated as,

  $\begin{array}{c}G\left(-x\right)=\frac{3\left(-x\right)+\left|-x\right|}{-x}\\ =\frac{-3x+x}{-x}\\ =2\end{array}$

The range of the function is calculated as,

  $\begin{array}{c}G\left(x\right)=\frac{3\left(x\right)+\left|x\right|}{x}\\ =\frac{3x+x}{x}\\ =4\end{array}$

The domain of the given function is all real values except $x\ne 0$ and the range of the function is $2\text{or}\text{4}$ .

Consider the graph of the given function,