Do Now Determine the open intervals over which the following function is increasing, decreasing, or constant. F(x) = | x + 1| + | x – 1| Determine whether the function is even, odd, or neither. Why? F(x) = x3 – 2x

P-9 Combinations of Functions

Arithmetic Combinations of Functions Just as 2 real numbers can be combined by the operations of +, -,X, ÷ to form other real numbers, 2 functions can be combined to create new functions.

Example f(x) = 2x – 3g(x) = x 2 – 1 Find (f+g) x Find (f-g) x The domain of an arithmetic combination of functions f & g consists of all real #’s that are common to the domain of f & g. x 2 + 2x - 4 -x 2 + 2x - 2 Find (fg)xx 3 -3x 2 + 2x - 3 Find f(x) g(x) 2x - 3 x 2 - 1

f(x) = x 2 + 3x g(x) = 3x – 7 Find (f+g)x Find (f-g)x Find (fg)x Find f/g(x)

Composition of functions Another way of combining two functions is to form the composition of one with the other. Written— F(g(x)) or f ◦ g (x)

Example f(x) = x 2 g(x) = x + 1 Find the f(g(x))(x + 1) 2 = x 2 + 2x + 1 Find the g ◦ f (x) x 2 + 1

Homework Thursday HW– Page 104 (5-23 odd) Friday HW– Page 105 (31-45 odd)