Chapter 4.7, Problem 12E

To determine

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

Answer to Problem 12E

The graph of $g\left(x\right)=-3x^6$ can be found by stretching the graph of $f\left(x\right)=x^6$ by a factor of $3$ units vertically followed by a reflection about $x$ axis.

Explanation of Solution

Given information:

Given functions are,

  $f\left(x\right)=x^6$ and $g\left(x\right)=-3x^6$

Concept used:

The graph of $g\left(x\right)=-af\left(x\right)$ can be found by stretching the graph of $f\left(x\right)$ by a factor of $a$ units vertically followed by a reflection about $x$ axis.

Calculation:

Consider the given functions.

  $f\left(x\right)=x^6$ and $g\left(x\right)=-3x^6$

The function $g\left(x\right)=-3x^6$ is of the form $g\left(x\right)=-af\left(x\right)$ where $a=3$ .

So, the graph of $g\left(x\right)=-3x^6$ can be found by stretching the graph of $f\left(x\right)$ by a factor of $3$ units vertically followed by a reflection about $x$ axis.

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