Chapter 2, Problem 56RE

To determine

To sketch: the graph of the function. Also state the domain, intercepts and range of the graph.

Answer to Problem 56RE

The range is $\left\{y|y\ge 4\right\}$ .

The domain of function $f\left(x\right)=\left|x\right|+4$ is the set of all real numbers.

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=\left|x\right|+4$

Calculation:

Let us consider the following function

  $f\left(x\right)=\left|x\right|+4$

The function $f\left(x\right)=\left|x\right|+4$ has the same shape as the graph of $g\left(x\right)=\left|x\right|$ .

The graph of $f\left(x\right)=\left|x\right|+4$ is the vertical shift of 4 units upwards.

The graph $f\left(x\right)=\left|x\right|+4$ is plotted below using Maple.

  

From the graph we see the domain of function $f\left(x\right)=\left|x\right|+4$ is the set of all real numbers. $f\left(x\right)$ can take any values greater than or equal to 4. Hence the range is $\left\{y|y\ge 4\right\}$ .