Part A: Knowledge & Understanding 23 marks 1. Given (x) = x3 + 4x - 5 and g (x) = x - 2, determine the following as a function of x in simplified farm: a) (f+ 9)(x) b) (9 - /)(x) c) ( x g)(1) d) - (x) 3. At 4:45 pm, a transport truck containing a fine clay powder was damaged slightly during a traffic accident and its under the truck in such a way that the ratio of height of the cone to its radius remained constant at 3:16. The driver noticed that the height of the cone was e) (f . g) (x) n (9 1 . )(x) Express the height of the cone, h, as a function of its radius, r. (1) bj Write a function, V(/), the volume of me in terms of it, the height. [1] Given f (x) = x+ 3, g(x) = x3 + 5x + 6, and h(x) = vx+ 1, Determine algebraically the equation for (f - A) (x). and state its domain. c) Write a function, A([), the height of the cone in terms of t. the time. [11 b) Determine algebraically the equation for (g . /)(x), and state its domain. d) Use composition of functions to determine the function V (f). e) What would be the volume of the clay power lost from the truck in half an hour? c) Determine algebraically the equation for & (x), and state its domain. 3. For the functions fix) and g(x) are given in the graph below. Find the indicated corresponding function values. [6] Part D: TIPS. Show work of good form! 10 marks a) ( + 9)(1)= 3. Create a linear function f(x) and a quadratic function g(x) such that it satisfies the following two conditions: (5] f + gl(x) = 4x2 + 30x + 39 (f - 9)(x) = -4x3 - 16x +6 b) (f - 9)(2) = c) (f + 9)(0) - d) ( x 9)(5) = e) (f-1-8-1)(-1) = I |Pagc 3|Page 4. Let f(x) = x- 1 and a(x) = -2x -5, find x such that fog =gcf . 13] 10 . If f (x ) = 2-38+4, show that f- 1 of = f of"1 = x. Part B: Application. Show work of good form! 15 marks 5. Letf = [(-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+ 9 6. Given f(x) and g(x) on the following grid, use the "superposition" principle to draw h(x) = f (x) - 9(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 /(x) and g(x)