Chapter 6.4, Problem 13E

To determine

To find: The function of $f$ represented by $g$ and draw the graph.

Answer to Problem 13E

The graph of the functions are increases exponentially starting from $\infty$ and graph of g(x) is shifted down by 6.

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=e^{-x}$ and $g\left(x\right)=e^{-x}+6$ .

Consider thegiven functions are $f\left(x\right)=e^{-x}$ and $g\left(x\right)=e^{-x}+6$ .

Write the function of $f$ in terms of the function $g$

  $\begin{array}{c}g\left(x\right)=e^{-x}+6\\ g\left(x\right)=f\left(x\right)+6\\ f\left(x\right)=g\left(x\right)-6\end{array}$

Now, draw the graph.

  

Hence, the graph of the functions are increases exponentially starting from $\infty$ and graph of g(x) is shifted down by 6.