Chapter 1.4, Problem 27E

To determine

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

Explanation of Solution

Given:

The given function is:

  $f(x)=x^2-2$

Calculation for graph:

Consider $f(x)=x^2-2$

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

Using the above table the graph can be plotted.

Graph:

  

Interpretation:

Hence, the parent function will be $g(x)=x^2$ .

Calculation for graph:

Consider $g(x)=x^2$

Values of x	Values of g (x )
0	0
1	1
-1	1
2	4
-2	4

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 vertical shift of 2 units downward.