Question

In Problems 27– 40, use transformations of the graph of $y=x^{4}ory=x^5$to graph each function. Verify your results using a graphing utility.

role="math" localid="1646158350708" $f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5-2$

Short answer

The graph is obtained by shifting one unit right, compressed by a factor of$\frac{1}{2}$and below 2 units.

Step-by-step solution

Step 1. Given Information

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

Step 2. Draw the graph of fx=x5

Step 3. Draw the graph of fx=x-15

Shift the graph of$f\left(x\right)=x^5$one unit right

Step 4. Draw the graph of 12x-15

Compress the graph of$f\left(x\right)={\left(x-1\right)}^5$by a factor of$\frac{1}{2}.$

Step 5. Draw the graph of fx=12x-15-2

Shift the graph of$f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5$two units below