Chapter 9.3, Problem 28PPS

To determine

List the function in order most stretched vertically to the least stretched vertically.

Answer to Problem 28PPS

The function in order from most stretched vertically to the least compressed is $h(x),g(x),\text{and}f(x)$

Explanation of Solution

Given:

The Functions: $g(x)=-x^2;h(x)=\frac{5}{3}{x}^2\text{and}f(x)=-4.5x^2$

Concept Used:

The functions can be written as $f(x)=a{x}^2$ 2.

For $g(x)=-x^2$ , $a=1$ , so the graph is neither stretched nor compressed.

For $h(x)=\frac{5}{3}{x}^2$ , $a=\frac{5}{3}$ , so the graph is stretched vertically.

For $f(x)=-4.5x^2$ , $a=4.5$ , so that graph is stretched vertically.

Since $4.5>\frac{5}{3};$ $f(x)$ is more stretched than $h(x)$ .

Therefore, the function in order from most stretched vertically to the least compressed is $f(x),h(x),\text{and}g(x)$

Thus, the function in order from most stretched vertically to the least compressed is $h(x),g(x),\text{and}f(x)$