Q. 40 - 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.

$f\left(x\right)=3-{\left(x+2\right)}^4$

Step-by-Step Solution

Answer

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

Step 1. Given Information

The given function is$f\left(x\right)=3-{\left(x+2\right)}^4=-{\left(x+2\right)}^4+3$

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

Step 3. Graph of f x = x + 2 4

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

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

Reflex the graph of $f\left(x\right)={\left(x+2\right)}^4$about x-axis

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

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