Chapter 4.7, Problem 4E

To determine

To describe: the transformation of $f$ represented by $g$ . Graph the functions $f$ and $g$ .

Answer to Problem 4E

The graph of $g\left(x\right)={\left(x-5\right)}^4$ can be found by translating the graph of $f\left(x\right)=x^4$ by $5$ units right horizontally.

Explanation of Solution

Given information:

Given functions are,

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

Concept used:

The graph of $g\left(x\right)=f\left(x-h\right)+k$ can be found by translating the graph of $f\left(x\right)$ by $k$ units up vertically and $h$ units right horizontally.

Calculation:

Consider the given functions.

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

The function $g\left(x\right)={\left(x-5\right)}^4$ is of the form $g\left(x\right)=f\left(x-h\right)+k$ where $h=5,k=0$ .

So, the graph of $g\left(x\right)={\left(x-5\right)}^4$ can be found by translating the graph of $f\left(x\right)=x^4$ by $5$ units right horizontally.

Now, sketch both the graphs in same set of axes as shown: