Chapter 9.1, Problem 18PPE

To determine

The order of the given functions from widest to narrowest.

Answer to Problem 18PPE

  $f\left(x\right)=-\frac{1}{4}{x}^2>f\left(x\right)=-\frac{1}{2}{x}^2>f\left(x\right)=5x^2$

Explanation of Solution

Given:

The given functions are:

  $\begin{array}{l}f\left(x\right)=-\frac{1}{2}{x}^2\\ f\left(x\right)=5x^2\\ f\left(x\right)=-\frac{1}{4}{x}^2\end{array}$

Calculation:

The graphs of the given functions can be drawn as:

  

The order from widest to narrowest will be:

  $f\left(x\right)=-\frac{1}{4}{x}^2>f\left(x\right)=-\frac{1}{2}{x}^2>f\left(x\right)=5x^2$