Chapter 7.4, Problem 38E

To determine

To find: The transformed form of the function $g\left(x\right)$ in the form $g\left(x\right)=\frac{a}{x-h}+k$ and graph the function. Then describe the graph of $g$ as the function of $f\left(x\right)=\frac{a}{x}$ .

Answer to Problem 38E

The transformed form is $g\left(x\right)=\frac{-79}{x+10}+7$ and the graph is shown in Figure 1 and the graph $g$ as the function of $f\left(x\right)=\frac{a}{x}$ is $f\left(x\right)=\frac{-79}{x}$ .

Explanation of Solution

Given:

The given function is $g\left(x\right)=\frac{7x-9}{x+10}$ .

Calculation:

Consider the given function is,

  $g\left(x\right)=\frac{7x-9}{x+10}$

Solve the above function as,

  $x+10\begin{array}{c}\hfill 7\\ \hfill \overline{)\begin{array}{l}7x-9\\ -\underset{\_}{\left(7x-70\right)}\\ -79\end{array}}\end{array}$

Then,

  $g\left(x\right)=\frac{-79}{x+10}+7$

The graph of the $g\left(x\right)$ is the translation of 10 unit to the left and 7 unit in upward direction of the graph of $f\left(x\right)$ as,

  $f\left(x\right)=\frac{-79}{x}$

Thus, the required graph is shown in Figure 1

  

Figure 1