The domain of a function $f$ is $x > 0$. The range of $f$ is $−2 < y ≤ 5$. 

1. Sketch a possible graph of $f$.

   Hint (a):

   Answers vary. Be creative. Just remember to stay within the dotted lines, which represent the domain and range.

2. What are the domain and range of $y = f(x - 2) +1$?

   Hint (b):

   The function you drew in part (a) will be shifted two units to the right and one unit up. Its domain and range will shift with it.

3. What are the domain and range of $f^{ -1}$?

   Hint (c):

   For inverse functions: Not only do the the $x$- and $y$-values switch, the domain and range switch as well.