Chapter 4, Problem 1CT

To determine

To graph: The function $f\left(x\right)={\left(x-3\right)}^4-2$ using transformations.

Explanation of Solution

Given information:

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

Graph:

Now, to graph the function $f\left(x\right)={\left(x-3\right)}^4-2$ using transformations.

First consider the graph of a parent function $y=x^4$ .

  

Then, by shifting the graph of $y=x^4$ to the right by $3$ units to get a graph of $y={\left(x-3\right)}^4$ shown below;

  

The graph of $y={\left(x-3\right)}^4-2$ is obtained by shifting the graph of $y={\left(x-3\right)}^4$ down to $2$ units

shown below;

  

Interpretation:

The above graph represents the function $y={\left(x-3\right)}^4-2$ .