Chapter 3.5, Problem 25PPS

To determine

The transform of given function from $f(x)$ to $g(x)$ .

Explanation of Solution

Given:

  $f(x)=x$

  $g(x)=\frac{7}{16}x$

Calculation for graph:

Consider $f(x)=x$

Values of x	Values of f(x)
0	0
-1	-1
1	1
2	2
-3	-3

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

Calculation for graph:

Consider $g(x)=\frac{7}{16}x$

Values of x	Values of g(x)
0	0
16	7
32	14
48	21
64	28

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

Graph:

  

Interpretation:

From the above graph, it is clear that,

  $f(x)=x$ is the parent graph and

  $g(x)=\frac{7}{16}x$ is a non-rigid transform of the parent graph with a vertical shrink of $\frac{7}{16}$ times of the values of the parent graph.