Chapter 1.6, Problem 41E

Solution

a.

The vertical stretch by a factor of 2 in function $f\left(x\right)=x^2+x-2$ .

The function after vertical stretch by a factor of 2 is $2x^2+2x-4$ .

Given:

  $f\left(x\right)=x^2+x-2$

Calculation:

  $f\left(x\right)=x^2+x-2$

Vertical stretch by a factor of 2:

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

b.

The horizontal shrink by a factor of $\frac{1}{3}$ in function $f\left(x\right)=x^2+x-2$ .

The function after horizontal shrink by a factor of $\frac{1}{3}$ is $9x^2+3x-2$ .

Given:

  $f\left(x\right)=x^2+x-2$

Calculation:

  $f\left(x\right)=x^2+x-2$

Horizontal shrink by a factor of $\frac{1}{3}$ :

  $\begin{array}{l}f\left(\frac{x}{\frac{1}{3}}\right)=f\left(3x\right)\\ f\left(\frac{x}{\frac{1}{3}}\right)={\left(3x\right)}^2+3x-2\\ f\left(\frac{x}{\frac{1}{3}}\right)=9x^2+3x-2\end{array}$