Chapter 3.5, Problem 29PPS

To determine

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

Explanation of Solution

Given:

  $f(x)=x$

  $g(x)=-7x-5$

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 $g(x)=-7x-5$

Values of x	Values of g(x)
0	-5
1	-12
2	-19
3	-26
4	-33

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

  $g(x)=-7x-5$ is a non-rigid transform of the parent graph with a vertical shift of 5 units to the downward after taking the reflection of base graph about x-axisand vertically stretching the obtained graph by 7 times.