Aim: How do we do arithmetic with functions? Do Now: Given polynomials 3x – 3 and x2 –1, find a. Simplify:(3x – 3)+(x2 – 1) HW: p.154 # 5,7,8-12,14 b. Simplify:(3x – 3) – (x2 – 1) c. Multiply:(3x – 3)(x2 – 1) d. Divide:

If we let f(x) = 3x – 3 and g(x) = x2 – 1 How do we do the 4 operations for these two functions? To do the operations of functions, we just treat each function as a polynomial expression f(x) ∙g(x) = (3x – 3)(x2 – 1) = 3x3 – 3x2 – 3x + 3 f(x) – g(x) = (3x – 3) – (x2 – 1) = – x2 + 3x – 2 f(x) + g(x) = (3x – 3) + (x2 – 1) = x2 + 3x – 4

(f/g)(x) = f(x)/g(x), g(x) not = 0 We can express these operations in another way: (f + g)(x) = f(x) + g(x) (f – g)(x) = f(x) – g(x) (fg)(x) = f(x) ∙ g(x) (f/g)(x) = f(x)/g(x), g(x) not = 0 The last operation is af(x), where a is a constant Let f(x) = 3x2 – 2x –1, a = 6 then af(x) = 6(3x2 – 2x – 1) = 18x2 – 12x – 6

Given f(x) = x – 3 and g(x) = x2 – 2x – 3 find: 1. (f + g)(x) 2. (f - g)(x) 3. (fg)(x) 4. (f/g)(x) 5. (g + f)(x) 6. (g - f)(x) 7. (gf)(x) 8. (g/f)(x)

Given h(x) = 8x3 - 4x2 and k(x) = 4x find: 192 9. (h + k)(3) 10. (h - k)(2) 11. (hk)(-2) 12. (h/k)(5) 13. (k - h)(2) 14. (k/h)(1) 40 640 45 -40 1