Chapter 1.4, Problem 38E

To determine

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

Explanation of Solution

Given:

The given function is:

  $f(x)=-x$

Calculation for graph:

Consider $f(x)=-x$

Values of x	Values of f (x )
0	0
1	-1
2	-8
-2	8
-1	1

Using the above table the graph can be plotted.

Graph:

  

Interpretation:

Hence, the parent function will be $g(x)=x^3$ .

Calculation for graph:

Consider $g(x)=x^3$

Values of x	Values of g (x )
0	0
1	1
4	64
-2	-8
-3	-27

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 transform function $g(x)$ and is the reflexion of the $g(x)$ about x- axis.