Chapter 10, Problem 4CA

To determine

To find: The statement which describes the transformation of the graph

Answer to Problem 4CA

The statement $A$ and $E$ describe the transformation of graph $f(x)=x^3-x$ represented by $g(x)=4{(x-2)}^3-4(x-2)$ .

Explanation of Solution

Given:

  $f(x)=x^3-x$

  $g(x)=4{(x-2)}^3-4(x-2)$.

Calculation:

The given statement describe the transformation graph $f(x)=x^3-x$ represented by $g(x)=4{(x-2)}^3-4(x-2)$ .

The function

  $\begin{array}{l}g(x)=4{(}^x-4(x-2)\\ g(x)=4\left[{(x-2)}^3-(x-2)\right]\end{array}$

Hence, the function of the form

  $g(x)=a\left[{(x-h)}^3-(x-h)\right]$

Thus, $h=2$ and $a=4$ .

Since $h=2$ , the graph of $g$ is a horizontal translation 2 units right of the graph of $f$ .

Since, $a=4$ , graph of g $g$ is a vertical stretch by a factor of 4 of the graph of $f$ .

Thus, the statement $A$ and $E$ describe the transformation of graph $f(x)=x^3-x$ represented by $g(x)=4{(x-2)}^3-4(x-2)$ .

Conclusion:

Therefore, the statement $A$ and $E$ describe the transformation of graph $f(x)=x^3-x$ represented by $g(x)=4{(x-2)}^3-4(x-2)$ .