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?

   Answer (c):

   $(0,−2)\ \text{and}\ (1.585,0)$

4. Change the equation so that the graph of the new equation has no x-intercepts.

   Hint (d):

   What is the value in the original equation that causes it to have an x-intercept?
   How can you change it so that the new equation will not have an x-intercept?