1. does the function show a direct linear variation, quadratic variation, or inverse variation? explain.

a. f (x) + 1/8 x^2

b. xy = 9

c. p (x) = x/11

2. the amount of time, t, miranda spends cross-country skiing varies directly with the number of miles, m, she skis. suppose miranda skis 2 mi in 0.5 h. a. write a direct variation equation relating this information. b. use your direct variation equation from part a to determine how much time it takes miranda to ski 5.2 mi.

3. the length, d, of a violin string varies inversely as the frequency, f, of its vibrations (cycles per second). suppose it is known that a 16-in.-long violin string vibrates 320 cycles per second. a. write an inverse variation equation modeling this information. b. use your inverse variation equation from part a to determine the frequency of an 8-in.-long violin string.