Chapter 3.5, Problem 35PPS

To determine

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

Explanation of Solution

Given:

  $f(x)=x$

  $g(x)=-2x-6$

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 $g(x)=-2x-6$

Values of x	Values of g(x)
0	-6
-4	2
4	-14
2	-10
1	-8

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

  $g(x)=-2x-6$ is a non-rigid transform of the parent graph with a vertical stretch of 2 times the base graph values and shifting the base graph vertically 6 units to the downward after taking the reflection about x-axis.