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="1646158372870" $f\left(x\right)=4-{\left(x-2\right)}^5$

Short answer

The graph is obtained by shifting 2 units right, reflex about x-axis and then 4 units up.

Step-by-step solution

Step 1. Given Information

The given function is$f\left(x\right)=4-{\left(x-2\right)}^5=-{\left(x-2\right)}^5+4$

Step 2. Draw the graph of fx=x5

Step 3. Draw the graph of fx=x-25

Shift the graph of $f\left(x\right)=x^5$two units right

Step 4. Draw the graph of fx=-x-25

Reflect the graph of $f\left(x\right)={\left(x-2\right)}^5$about x-axis

Step 5. Draw the graph of fx=-x-25+4

Shift 4 units up the graph of$f\left(x\right)=-{\left(x-2\right)}^5$