Q. 37 - 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.

$f\left(x\right)=2{\left(x+1\right)}^4+1$

Step-by-Step Solution

Answer

The graph is obtained by shifting one unit left, stretched by factor 2 and shift one unit above.

Step 1. Given Information

The given function is$f\left(x\right)=2{\left(x+1\right)}^4+1$

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

Step 3. Draw the graph of f x = x + 1 4

Shift one unit left of the graph of $f\left(x\right)=x^4$

Step 4. Draw the graph of 2 x + 1 4

Stretch the graph of ${\left(x+1\right)}^4$ by factor 2

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

Shift the graph of $f\left(x\right)=2{\left(x+1\right)}^4$ one unit up