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

1. Find 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. Find the equation of the line tangent to the graph of $y =\operatorname{log}_2 x$ at its $x$-intercept.

   Hint (b):

   Refer to hint in part (a).

3. Graph both of these 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 under or over approximation of the actual value? How do you know using concavity?

   Hint (d):

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