A swimmer crosses a pool of width b by swimming in a straight line from (0, 0) to (2b, b). (See figure.)

(a) Let ƒ be a function defined as the y-coordinate of the point on the long side of the pool that is nearest the swimmer at any given time during the swimmer's crossing of the pool. Determine the function ƒ and sketch its graph. Is ƒ continuous? Explain. 

(b) Let g be the minimum distance between the swimmer and the long sides of the pool. Determine the function g and sketch its graph. Is g continuous? Explain.

Transcribed Image Text:

(0, 0) (2b, b) b X