Chapter SH, Problem 9.3.13EP

To determine

To find:Theorder of the functions.

Answer to Problem 9.3.13EP

The order of the functions is $g\left(x\right)=-x^2>h\left(x\right)=\frac{5}{3}{x}^2>f\left(x\right)=-2\cdot 5x^2$ .

Explanation of Solution

Given information:

The order of the functions is $g\left(x\right)=-x^2>h\left(x\right)=\frac{5}{3}{x}^2>f\left(x\right)=-2\cdot 5x^2$ .

Calculation:

Consider the function $g\left(x\right)=a{x}^2$ .

In the graph of the function, the graph stretched vertically if $\left|a\right|>1$ and is compressed vertically if $0<\left|a\right|<1$

In the function

  $\begin{array}{c}h\left(x\right)=\frac{5}{3}{x}^2\\ a=\frac{5}{3}=1\cdot 66\end{array}$

The graph stretched vertically if $\left|a\right|>1$

In the function

  $\begin{array}{c}f\left(x\right)=-2\cdot 5x^2\\ a=2\cdot 5\end{array}$

The graph that is most compressed is $g\left(x\right)=-x^2$ .

Then the next graph is most compressed is $h\left(x\right)=\frac{5}{3}{x}^2$ as its value of coefficient $a$ is less than $a=2\cdot 5$ .

The order is $g\left(x\right)=-x^2>h\left(x\right)=\frac{5}{3}{x}^2>f\left(x\right)=-2\cdot 5x^2$ .

Therefore, the order of the functions is $g\left(x\right)=-x^2>h\left(x\right)=\frac{5}{3}{x}^2>f\left(x\right)=-2\cdot 5x^2$ .