Chapter 4.7, Problem 58HP

To determine

To find:The domain and range from the given graph.

Answer to Problem 58HP

The absolute value function of the given graph is $y=\left|x-6\right|$ . The domain is $-\infty <x<\infty$ and the range is $f\left(x\right)\ge 0\text{ or }[0,\infty )$

Explanation of Solution

Given:

The given graph is

  

Calculation:

To write the absolute value function for the graph, observe the given graph. It can be seen that the graph is shifted towards right by the units 6. The upward shift of the graph is zero that means k =0.

From the general function

  $\begin{array}{l}y=a\left|x-h\right|+k\\ a=1\left(\text{Graph is neither compressed nor expanded}\right)\\ k=0\left(\text{The upward shift of the graph is 0}\right)\\ h=6\left(\text{The graph is shifted to right by 6 points}\right)\\ y=1\left|x-6\right|+0\\ y=\left|x-6\right|\end{array}$

Therefore, the function for the graph is $y=\left|x-6\right|$ .

The set of input or argument values for which the function gives real and defined output is termed as the domain of the function. Find the domain from the given graph. In the given graph domain constraints and the undefined points are not observed. Therefore the domain of the graph is $-\infty <x<\infty$ .

The range is defined as the set of values of the dependent variables for which the function has defined values.

The range of the given function is $f\left(x\right)\ge 0\text{ or }[0,\infty )$ .

Therefore the domain of the graph is $-\infty <x<\infty$ and the range of the graph is $f\left(x\right)\ge 0\text{ or }[0,\infty )$ .