Make a table of $y=\frac{1}{2}x-3$ and its inverse function.

1. What is the relationship between the table for the original function and its inverse?

   Hint (a):

   What happens to the inputs and outputs when determining the inverse?

2. Graph $y=\frac{1}{2}x-3$ and its inverse function on the same set of axes.

   Hint (b):

   If you are stuck, use your tables from part (a).

3. What is the equation of the inverse function?

   Hint (c):

   What is being done to $x$ in the original function? Make a list and undo.

   Answer (c):

   Inverse: 

   1. Add 3                 $x+3$

   2. Multiply by 2     $2\left(x+3\right)$

        The inverse is $y=2\left(x+3\right)$

4. Does the graph of the two lines have a line of symmetry? If so, what is the equation of the line of symmetry?

   Hint (d):

   Can you fold the graph in half so that the lines coincide?