Lew walks every day at lunch when he is working. The amazing thing about Lew is that he walks at a constant rate (velocity) for the whole time he walks. He walks for $1$ hour every day and travels at a rate of $4$ miles per hour. 

1. Draw a graph of Lew’s lunchtime walk, being sure to label both axes. Shade the area between the curve $f(x)$ and the $x$­-axis over the appropriate domain.

   Answer (a):

   

2. Explain why the domain will only be between $0$ and $1$. What is the range of this function?

   Answer (b):

   The domain is time elapsed, and Lew walks for one hour. The range is $4$ miles per hour.

3. The figure that is shaded on your graph should resemble a rectangle. Using unit analysis and the units from each axis, find the resulting units when you find the area of the rectangle.

   Answer (c):

   The units are miles since:

   $\frac{\text{miles}}{\text{hour}}\cdot \text{hr}=\text{miles}$

4. Find the area of the shaded region. Include the proper units.

   Hint (d):

   Use the graph above to figure this out.