Chapter 1.4, Problem 26E

To determine

To compare the graph of the given function with the parent function

Explanation of Solution

Given:

The given function is:

  $f(x)=|x+5|$

Calculation for graph:

Consider $f(x)=|x+5|$

Values of x	Values of f (x )
0	5
-1	4
1	6
2	7
-2	3

Using the above table the graph can be plotted.

Graph:

  

Interpretation:

Hence, the parent function will be $g(x)=\left|x\right|$ .

Calculation for graph:

Consider $g(x)=\left|x\right|$

Values of x	Values of g (x )
0	0
1	1
-1	1
2	2
-2	2

Using the above table the graph can be plotted:

Graph:

  

Interpretation:

To compare the functions, the graph of both $f(x)$ and $g(x)$ are plotted on a same co-ordinate plane.

Graph:

  

Interpretation:

From the above graph, it is clear that,

  $f(x)$ is the rigid transformation of the parent function $g(x)$ with a horizontal shift of 5 units to the left