Question

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

role="math" localid="1646150128599" $f\left(x\right)={\left(x-2\right)}^5$

Short answer

The graph of the function $f\left(x\right)={\left(x-2\right)}^5$is shown in the figure.

Step-by-step solution

Step 1. Given Information

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

Step 2. Draw the graph of fx=x5

Then move the graph to two unit rights of origin, we get the graph of$f\left(x\right)={\left(x-2\right)}^5$

Step 3. By using Graphing utility

Make a table for values of $x,y$

$x$	$-2$	$-1$	$0$	1
$f\left(x\right)={\left(x-2\right)}^5$	$-1024$	$-243$	$-32$	$-1$

Connect all these points on the graph, you will get the desired result.