Chapter 1.4, Problem 8E

To determine

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

Explanation of Solution

Given:

The given functions are:

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

Calculation for graph:

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

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

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	2
1	2.5
-1	-1.5
2	3
-2	1

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

Calculation for graph:

Consider $h(x)=4(x-2)$

Values of x	Values of h (x )
0	-8
1	-4
-1	-12
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, $y=x$ is the base graph.

  $f(x)$ is the non-rigid transformation of the base graph.

  $g(x)$ is the non-rigid transformation of the base graph with a vertical shift of 2 units upwards

  $h(x)$ is the non-rigid transformation of the base graph with a horizontal shift of 2 units right side.