1. 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:

2. 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

3. (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 = then af(x) = 6(3x2 – 2x – 1) = 18x2 – 12x – 6

4. 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)

5. 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