Chapter 1.4, Problem 9E

To determine

To sketch the graph of the given functions on same co-ordinate system

Explanation of Solution

Given:

The given functions are:

  $\begin{array}{l}f(x)=x^2\\ g(x)=x^2+2\\ $ h(x)={(x-2)}^2$\end{array}$

Calculation for graph:

Consider $f(x)=x^2$

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

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

Calculation for graph:

Consider $g(x)=x^2+2$

Values of x	Values of g (x )
0	2
1	3
-1	3
2	6
-2	6

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

Calculation for graph:

Consider $h(x)={(x-2)}^2$

Values of x	Values of h (x )
0	4
1	1
-1	4
2	0
-2	16

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

Graphs on the same co-ordinate system:

  

Verification:

Using graphing utility to draw the graph of given functions,

  

Interpretation:

From above graph, it is clear that, the drawn sketch and above graph are identical to each other.

Here, $f(x)=x^2$ is the base graph.

  $g(x)$ is the rigid transformation of $f(x)$ with a vertical shift of 2 units upward.

  $h(x)$ is the rigid transformation of $f(x)$ with the horizontal shift of 2 units to the right.