Chapter 3.5, Problem 34PPS

To determine

To describe the transform of given function from $f(x)$ to $g(x)$ .

Explanation of Solution

Given:

  $f(x)=x$

  $g(x)=0.2(x+9)$

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 $g(x)=0.2(x+9)$

Values of x	Values of g(x)
0	1.8
-1	1.6
1	2
2	2.2
-3	1.4

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

  $g(x)=0.2(x+9)$ is a non-rigid transform of the parent graph with a vertical shrink of 0.2 times the base graph values and shifting the base graph vertically 1.8 units to upwards.