Q. 35 - 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.

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

Step-by-Step Solution

Answer

The graph is obtained by moving one unit right and then 2 unit up from the graph of $f\left(x\right)=x^5$.

Step 1. Given Information

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

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

Step 3. Draw the graph of f x = x - 1 5

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

Step 4. Draw the graph of f x = x - 1 5 + 2

Move 2 unit up the graph of $f\left(x\right)={\left(x-1\right)}^5$