Quickly sketch the function
You should recognize this function as a semicircle with radius
State the domain and range of
Consider the radius and center of the semicircle. This should help you determine domain and range?
Use geometry to find
On the graph of
, shade the region . Observe that this area is the area of a complete circle, and the area of the semicircle, .
You can use your answer to part (b) and help answer part (c).
What is the relationship between the answers of (b) and (c)?
The area in (c) is double the area in (b). Be sure to confirm this numerically.