Creating Models A swimmer crosses a pool of width b by swimming in a straight line from (0,0) to (2 b, b ). (See figure.) (a) Let f 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 f and sketch its graph. Is f 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.
Creating Models A swimmer crosses a pool of width b by swimming in a straight line from (0,0) to (2 b, b ). (See figure.) (a) Let f 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 f and sketch its graph. Is f 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.
Solution Summary: The author analyzes the function f with given conditions and sketching its graph and continuity.
Creating Models A swimmer crosses a pool of width b by swimming in a straight line from (0,0) to (2b, b). (See figure.)
(a) Let f 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 f and sketch its graph. Is f 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.
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