3. For the functions f(x) and g(x) are given in the graph below. Find the indicated corresponding function values. [6] a) (f + g) (1)= b) (f - g) (2) = c) (f = g)(0) = d) (f * g)(5) = e) (f-1 -9-1)(-1) = 1 |Page 4. Let f(x) = x -1 and g(x) = -2.x? -5, find x such that fog =go f . [3] Part B: Application. Show work of good form! 15 marks 5. Let f = ((-4,4), (-2,4), (1,3), (3,5), (4,6)) and g = [(-4,2). (0,2), (1,2), (2,2), (4,4)}. Determine [3] [a)f+ g [ b) f - g c) g - f 6. Given f(x) and g(x) on the following grid, use the "superposition" principle to draw h(x) = f (x) - g(x). [3] 7. Let f(x) = mx2 + 2x + 5 and g(x) = 2x2 - nx - 2. The functions are combined to form the new function h(x) = f(x) + g(x). Points (1, 6 ) and (-1,10) satisfy the new function. Determine f(x) and g(x). [4] 2|Page 8. At 4:45 pm, a transport truck containing a fine clay powder was damaged slightly during a traffic accident and its contents were slowly leaking out. A cone-shaped pile was forming under the truck in such a way that the ratio of the height of the cone to its radius remained constant at 3:16. The driver noticed that the height of the cone was increasing by 3 cm every 8 minutes. a) Express the height of the cone, h, as a function of its radius, r. [1] b) Write a function, V(h), the volume of the cone in terms of h, the height. [1] c) Write a function, h(t), the height of the cone in terms of t, the time. [1] d) Use composition of functions to determine the function V (t). [1] e) What would be the volume of the clay power lost from the truck in half an hour? [1] Part D: TIPS. Show work of good form! 10 marks 9. Create a linear function f(x) and a quadratic function g(x) such that it satisfies the following two conditions: [5] f + 9)(x) = 4x2 + 30x + 39 (f - g)(x) = -4x2 - 16x + 6 3|Page 10. If f(x) = 2-3x+4, show that fl of = f of-1 = x. [5]