Chapter 1.4, Problem 17E

To determine

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

Explanation of Solution

Graph:

The given functions are:

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

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 $g(x)=\sqrt{x+1}$

Values of x	Values of g (x)
0	1
3	2
8	3
-1	0
15	4

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

Calculation for graph:

Consider $h(x)=\sqrt{x-2}+1$

Values of x	Values of h (x )
2	1
3	2
11	4
18	5
27	6

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, $y=\sqrt{x}$ is the base graph.

  $f(x)$ is the rigid transformation of base graph and is reflection of the same about x -axis.

  $g(x)$ is the rigid transformation of base graph with horizontal shift of 1 unit to the left.

  $h(x)$ is the rigid transform of base graph with a horizontal shift of 2 units to the right and vertical shift of 1 unit upward.