Consider the function $h(x)=3(2)^x+1$.  

1. Describe $h(x)$ as a transformation of $y=2^x$.

   Hint (a):

   The function is vertically _____ by a factor of __ and shifted __ $1$ unit.

2. Sketch the graph of $y=h(x)$.

   Hint (b):

   This is an exponential growth function. The locator point is at $(0,?)$.

3. What is the equation of the horizontal asymptote?

   Hint (c):

   Use your graph from part (b). You can use a graphing calculator to verify that your graph is correct. If it is not, be sure to identify and correct any mistakes.

4. What is the $y$-intercept?

   Step (d):

   Solve: $y=3(2)^0+1$

5. What is the $y$-intercept of the graph of $y=a(2)^x+k$?

   Step (e):

   Solve: $y=a(2)^0+k$