16. A glider is launched from a tower on a hilltop. The height, in metres, is negative whenever the glider is below the height of the hilltop. The equation representing the flight is h(t) = 2(z 3) (r 12), where time, t, is measured in seconds. ht) Height (m) a) b) c) 30 20 10 y=h(t) 12 16 20 Time (s) What does h(0) represent? What does (3) represent? When is the glider at its lowest point? What is the vertical distance between the top of the tower and the glider at this time? 17. Babe Ruth, a baseball player, hits a "major league pop-up" so that the height of the ball, in metres, is modelled by the function b(r) = 1 + 30. 51, where ris time in seconds. a) Evaluate the function for each of the given times to complete the table of values below. b) Graph the function. c) When does the ball reach its maximum height? d) What is the ball's maximum height? e) How long does it take for the ball to hit the ground? Time (s) 00 05 10 15 20 25 3.0 35 40 45 5.0 5.5 6.0 6.5 7.0 75 8.0 Height (m) 191 9 : 1. Explain the meaning of f(3) = 2. Evaluate f(3) for each of the following. a) {(1,2), (2,0), (3, 1), (4,2)) c) b) X 1.3 Working with Function Notation 1 2 3 3 4 4 5 3. Determine f(-2), f(0). f(2), and f(2x) for each function. a) f(x) = -3x +5 b) f(x) = 4x - 2x + 1 4. A stone is thrown from a bridge into a river. The height of the stone above the river at any time after it is released is modelled by the function b(t) = 72- 4.9r. The height of the stone, h(t), is measured in centimetres and time, t, is measured in seconds. a) Evaluate (0). What does it represent? b) Evaluate b(2.5). What does it represent? c) If b(3) =27.9, explain what you know about the stone's position. t M 6 19 4 2 14 6 4- (1,3) 2- 0 (2,5) -2- -N 2 (3, 2) (4,0) 4 18 jedbook MCMO-Function > B ebookK MOES MG FORCTIO ontent/140820650/View d) Docs f(3) = 4 for this function? Explain. 13. The sum of two whole numbers is 10. Their product can be modelled by the function P(x) = x(10-x). T a) What does x represent? What does (10 x) represent? What does P(x) represent? b) What is the domain of this function? c) Evaluate the function for all valid values of the domain. Show the results in a table of values. 0 P(x) 0 d) What two numbers do you estimate give the largest product? What is the largest product? Explain. X 14. A farming cooperative has recorded information about the A relationship between tonnes of carrots produced and the amount of fertilizer used. The function f(x) -0.53x + 1.38x + 0.14 models the effect of different amounts of fertilizer, x, in hundreds of kilograms per hectare (kg/ha), on the yield of carrots, in tonnes. a) Evaluate f(x) for the given values of x and complete the table. Fertilizer, x (kg/ha) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Yield, y(x) (tonnes) b) According to the table, how much fertilizer should the farmers use to produce the most tonnes of of carrots! c) Check your answer with a graphing calculator or by evaluating f(x) for values between 1.25 and 1-50. Why does the answer change? Explain. Function Notation