Mathematics 30-1: Module 7 20 Lesson 5: Multiplying and Dividing Functions 1. Given f(x) = x - 3 and g(x) = -2x + 2, a. state the function h(x) = (f . g)(x) (2 marks) b. graph h(x) = (f . g)(x) (2 marks) toty 8 - 10 -8 - 6 -4 - 2 0 16 c. state the domain and range of the combined function h(x) = (f . g)(x) (2 marks) 2012 Alberta Education C ADVoluboM :1-08 agitemory Mathematics 30-1: Module 7 21 2. Given f(x) = x and g(x) = V4x-5, pagerie bris essie auchev ni omoo eoxod oniqgine a. determine h(x) = f(x)g(x) (1 mark) oar xat XAS 8609)V Jprod b. state the domain and range of h(x) (2 marks) 3. Given f (x) = x+2 and g(x) =x2 +9x+14, a. determine h(x) = | (x) in simplified form (2 marks) b . state the domain and range of h(x) (2 marks) 2012 Alberta EducationMathematics 30-1: Module 7 22 5. Shipping boxes come in various sizes and shapes. Consider a box with a square base, whose base length must be greater than 5 cm. The volume in cubic centimetres, V, of this box is given as V(x) = 3x3+24x2+15x-150. height * + 5 x +5 a. Write a combined function to represent the area of the base, A(x), if the side length of the base is x + 5. (2 marks) Determine the combined function h (x) = V X ; A (x ) in simplified form. (2 marks) What does this function h(x) represent in this context? (1 mark) 2012 Alberta EducationMathematics 30-1: Module 7 23 Lesson 6: Composition of Functions 1. Given f(x) = 3x + 1 and g(x) = x2, determine the simplified version of the following: a. f(g(2)) (2 marks) b. (fog)(x) (2 marks) c. (fo f) (x) (2 marks) 2. You make a purchase at a local furniture store, but what you bought is too big to take home in your car. You arrange to have the store deliver your purchase for you, for a reasonable fee. You pay for your purchase, plus the sales tax, plus the fee. The tax is 5% and the fee is $50. a. Write a function (x) for the total, after taxes, on the purchase amount x. (2 marks) b. Write another function f(x) for the total, including the delivery fee, on the purchase amount x. (2 marks) 2012 Alberta Education