Chapter 7.6, Problem 59PPS

To determine

To list the functions in order from most vertically stretched to the least vertically stretched.

Answer to Problem 59PPS

Most stretched function is $j(x)$ then $g(x)$ and finally $p(x)$

Explanation of Solution

Given:

The parent function: $f(x)=2^x$

  $g(x)=0.4{(2)}^x$

  $j(x)=4{(2)}^x$

  $p(x)=\frac{1}{4}{(2)}^x$

Calculation for graph:

Consider $f(x)=2^x$

Values of x	Values of f (x)
0	1
-1	0.5
1	2
2	4
3	8

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

Calculation for graph:

Consider $g(x)=0.4{(2)}^x$

Values of x	Values of g(x)
0	0.4
-1	0.25
1	0.8
2	1.6
3	3.2

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

Calculation for graph:

Consider $j(x)=4{(2)}^x$

Values of x	Values of j(x)
0	4
-1	2
1	8
2	16
3	32

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

Calculation for graph:

Consider $p(x)=\frac{1}{4}{(2)}^x$

Values of x	Values of p(x)
0	0.25
-1	0.125
1	0.5
2	1
3	2

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

Graph:

  

Interpretation:

The graph which is more nearer to y -axis, it will be more vertically stretched.

So, the most stretched function is $j(x)$ then $g(x)$ and finally $p(x)$ .