Chapter 5.8, Problem 7STP

Let $f(x)=|x-3|+1$

a. What is the graph of the function?

b. How is the graph related to the graph of $y=\left|x\right|$?

To determine

To graph the function $f(x)=|x-3|+1$ .

Explanation of Solution

Given:

Function: $f(x)=|x-3|+1$

Calculation for graph:

Consider $f(x)=|x-3|+1$

Values of x	Values of f (x )
0	4
1	3
2	2
3	1
4	2

By taking different values of x , the graph can be plotted.

Graph:

  

Interpretation:

From the graph it can be observed that the horizontal extent of the graph is from $-\infty$ to $\infty$ .

And the vertical extent of the graph is also from $1$ to $\infty$ .

So, both the domain of the function is $(-\infty ,\infty )$ and the range of the function is $(1,\infty )$

To determine

To determine the relation between $f(x)=|x-3|+1$ and $y=\left|x\right|.$

Answer to Problem 7STP

  $y=\left|x\right|$ is the parent function of the function $f(x)=|x-3|+1$

Explanation of Solution

Given:

Function: $f(x)=|x-3|+1$

3 is subtracted from the modulus part of the parent function of the graph is $y=\left|x\right|$ . So, the graph is transferred 3 unit right from the parent graph $y=\left|x\right|$ .

1 is added to the parent function of the graph is $y=\left|x\right|$ . So, the graph is transferred 1 unit up from the parent graph $y=\left|x\right|$ .

Conclusion:

Hence, the function $y=\left|x\right|$ is the parent function of the function $f(x)=|x-3|+1$ .