Q. 38 - 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.

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

Step-by-Step Solution

Answer

The graph is obtained by shifting one unit right, compressed by a factor of $\frac{1}{2}$ and below 2 units.

Step 1. Given Information

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

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 1 2 x - 1 5

Compress the graph of $f\left(x\right)={\left(x-1\right)}^5$ by a factor of $\frac{1}{2}.$

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

Shift the graph of $f\left(x\right)=\frac{1}{2}{\left(x-1\right)}^5$ two units below