Chapter 1.4, Problem 14E

To determine

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

Explanation of Solution

Given:

The given functions are:

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

Calculation for graph:

Consider $f(x)=\left|x\right|$

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

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

Calculation for graph:

Consider $g(x)=\left|2x\right|$

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

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

Calculation for graph:

Consider $h(x)=-2|x+2|-1$

Values of x	Values of h (x )
0	-5
1	-7
-1	-3
2	-5
-2	-1

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, $f(x)=\left|x\right|$ is the base graph.

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

  $h(x)$ is the non-rigid transformation of base graph with vertical stretch, horizontal shift of 2 unit towards left and reflection of the same about x -axis with a vertical shift of 1 unit downward.