MAT151 Exam 4 - Modules 14-16 1. A few years ago Sky Harbor Airport had the following parking rates for short-term parking: a. Create a piecewise function F(m). Parking Time Parking Fee (minutes) (dollars) F Over 0 through 60 4,00 Over 60 through 120 8.00 Over 120 10.00 Source: www.phsskyharbor.com b. Graph the function. 10 Fee (5) Minutes (m) 120 149 C. Evaluate F(40), F(76), F(480), and F(1800) F (40) = F (76) = F (480) = F(1800) = d. Solve F(m) = 4, and F(m) = 9 for m (Find the condition for m). 2. Given f(x) = vx + 3 and g(x) = , find f(g(x)) and g(f (x)). f(g(x)) = g(f ()) =3. Given the functions f(x) = -3x2 g(x) = 3x + 1 h(x) = 2x2 - 2 t(x) = vx Find the following: a. h(g(4)) b. g(t(25)) c. t(g(x)) 4. Use the tables to answer the following questions: a. f(g(2)) b. f-1(g(-2)) f(x) X g(x) .2 -2 0 -1 1 -2 3 c. f(f(0)) d. f(g-'(-2)) 0 -2 -1 2 5. A world-renowned seaside restaurant has an outstanding scallop dish on its menu. The number of fresh shellfish in the area has been decreasing due to the pollutants in the ocean. There are two related functions in this scenario. One is the number of scallops per acre, S, as a function of the amount of pollutants found in the ocean, p, in grams per liter, modeled by S(p) = 23 -4p. The second is the cost (in dollars) of a scallop dinner, C, as a function of the number of scallops per acre, s, modeled by C(s) = 39.95 - 1.10s. a. Determine the composite function C(S(p)) and explain what it defines in the context of the problem. b. How much did a scallop dinner cost before there were pollutants in the ocean? c. Solve C(S(p) ) = 21.50 and explain the meaning of the results in the context of the