Chapter 1.4, Problem 16E

To determine

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

Explanation of Solution

Given:

The given functions are:

  $\begin{array}{l}f(x)=\sqrt{x}\\ g(x)=\frac{1}{2}\sqrt{x}\\ h(x)=-\sqrt{x-4}\end{array}$

Calculation for graph:

Consider $f(x)=\sqrt{x}$

Values of x	Values of f (x )
0	0
1	1
4	2
9	3
16	4

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

Calculation for graph:

Consider $g(x)=\frac{1}{2}\sqrt{x}$

Values of x	Values of g (x)
0	0
1	0.5
4	1
9	1.5
16	2

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

Calculation for graph:

Consider $h(x)=-\sqrt{x-4}$

Values of x	Values of h (x )
4	0
5	-1
13	-3
20	-4
29	-5

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, $f(x)=\sqrt{x}$ is the base graph.

  $g(x)$ is the non- rigid transformation of base graph with a vertical shrink.

  $h(x)$ is the rigid transformation of base graph, which is the reflection of the same about

x -axis with a horizontal shift of 4 units to the right.