Chapter 1, Problem 7CA

To determine

To select: Possible transformations of the graph of $f$ represented by the function $g$ .

Answer to Problem 7CA

Transformations are $A\to E\to C$ .

Explanation of Solution

Given information: $f(x)=x,g(x)=-3x-4$ .

Calculation:

  $f(x)=x$

First reflect in the x-axis,

  $h(x)=-x$

Then shrink horizontally by a factor of $\frac{1}{3}$ ,

  $\begin{array}{l}j(x)=h(3x)\\ \\ j(x)=-3x\end{array}$

At last, translate $4$ units down,

  $\begin{array}{l}g(x)=j(x)-4\\ \\ g(x)=-3x-4\end{array}$

Thus, the transformations are $A\to E\to C$ .