Q. 28 - Precalculus Enhanced with Graphing Utilities

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.

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

Step-by-Step Solution

Answer

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

Step 1. Given Information

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

Step 2. Draw the graph of f x = x 5

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.