Consider the function $f(x) = \frac { 1 } { x - 4 }$.  

1. Sketch a graph of the function. Label any holes or asymptotes.

   Hint (a):

   No holes. Two asymptotes: $x = 4$ and $y = 0$. Label them.

2. Write an equation for the inverse of $f$. Is the inverse a function? Why or why not?

   Step 1 (b):

   $y=\frac{1}{x-4}\ \ \ \ \ \text{Rename }f(x)\text{ as }y$

   Step 2 (b):

   $y(x-4)=1 \ \ \ \text{solve for }x$

   $x-4=\frac{1}{y}$

   $x=\frac{1}{y}+4$

   Answer (b):

   $f^{-1}(x)=\frac{1}{x}+4 \ \ \ \text{Switch the }x \text{ and }y$

3. Sketch a graph of the inverse and compare this sketch to the graph of $y = f(x)$ from part (a).

   Hint (c):

   You do not need to know the inverse equation to sketch a graph of the inverse. Start by switching the horizontal and vertical asymptotes. Then plot some key points, and connect.