My post probably wont be as crazy long as the last one, but today we talked about combinations of functions. We learned the first four combinations which are arithmetic including the sum, difference, product and quotient.

Let f and g be two functions with overlapping domains. Then, for all x common to both domains, the sum, difference, product, and quotient of f and g are defined as follows:

use f(x) = x + 2 & g(x) = x² + 3 as an example

sum: (f + g)(x) = f(x) + g(x)

(x + 2) + (x² + 3)
= x² + x + 5

difference: (f - g)(x) = f(x) - g(x)

(x + 2) - (x² + 3)
= -x² + x - 1

> note: it is important to remember the parentheses when finding the difference of functions.

product: (f g)(x) = f(x) * g(x)

(x + 2)(x² + 3)
= x³ + 2x² + 3x + 5

quotient: (f /g)(x) = f(x) / g(x)

(x + 2) / (x² + 3)

> note: g(x) ≠ 0

next we will look into compositions of functions, but until then the homework for tonight is assignment 6 -
1.3 # 42, 53, 59, 63
1.4 # 1-25 odd, 26, 106-110 even

also happy birthday to those born on 9.28 -- Spencer Rogers

enjoy this birthday wish from Lauren, and that new kid Lily. http://www.youtube.com/watch?v=8Q45N-oNu-4