Sketch the graph of $y + 3 = 2^x$.

1. What are the domain and range of this function?

   Answer (a):

   Domain: all real numbers
   Range: $y > −3$

2. Does this function have a line of symmetry? If so, what is it?

   Answer (b):

   There is no line of symmetry.

3. What are the $x$- and $y$-intercepts?

   Hint (c):

   Use your graph to estimate the intercepts.

4. Sketch the inverse of this function on the same set of axes. What are the domain, range, and $x$- and $y$-intercepts of the inverse?

   Hint (d):

   Identify a few key points on the original graph and reverse their coordinates to create the graph of the inverse.