Sketch the graph of $y = 2^x$ and its inverse. Label all intercepts.

1. Write the equation of the line tangent to the graph of $y = 2^x$ at its $y$-intercept.

   Graph (a):

   

   Hint (a):

   Use point-slope form.

2. Write the equation of the line tangent to the graph of $y = \log_2(x)$ at its $x$-intercept.

   Hint (b):

   Refer to the hint in part (a).

3. Graph both of these tangent lines. What is their relationship?

   Hint (c):

   Sketch the tangent lines. Are they parallel? Are they perpendicular? Neither?
   Look at their equations... describe a pattern you see in their slopes.

4. Use the tangent line in part (a) to approximate the value of $y$ when $x = 0.1$. Is your estimate an underestimate or an overestimate of the actual value? How do you know?

   Hint (d):

   Recall that the concavity of the graph determines whether tangent lines lie above or below the curve.