Chapter 4.1, Problem 38AYU

In Problems 29-42, use transformations of the graph of $y=x^4$ or $y=x^5$ to graph each function.

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

To determine

To graph: Using transformation $y=x^5$ of the function $f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5-2$.

Answer to Problem 38AYU

$\text{Using transformation }y=x^5\text{ of the function }f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5-2\text{ is graphed}$.

Explanation of Solution

Given:

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

$y=x^5$

The first graph $=y=x^5$.

The second graph $=f\left(x\right)={\left(x-1\right)}^5$.

The third graph $=f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5$.

The fourth graph $=f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5-2$.