Q. 39 - 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.

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

Step-by-Step Solution

Answer

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

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 f x = x 5

Step 3. Draw the graph of f x = x - 2 5

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

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

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

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

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