Chapter 1.4, Problem 11E

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)=\frac{1}{2}{x}^2\\ $ h(x)={(2x)}^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 $g(x)=\frac{1}{2}{x}^2$

Values of x	Values of g (x)
0	0
1	0.5
-1	0.5
2	2
-2	2

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

Calculation for graph:

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

Values of x	Values of h (x )
0	0
1	4
-1	4
2	16
-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 non-rigid transformation of base graph with vertical shrink.

  $h(x)$ is the non-rigid transformation of base graph with horizontal shrink.