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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 – 3 g(x) = x2 – 1 Find (f+g) x x2 + 2x - 4 Find (f-g) x -x2 + 2x - 2 Find (fg)x Find f(x) g(x) x3 -3x2 + 2x - 3 2x - 3 x2 - 1 The domain of an arithmetic combination of functions f & g consists of all real #’s that are common to the domain of f & g. • f(x) = x2 + 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) = x2 Find the f(g(x)) Find the g ◦ f (x) g(x) = x + 1 (x + 1)2 = x2 + 2x + 1 x2 + 1 Homework • Thursday HW– Page 104 (5-23 odd) • Friday HW– Page 105 (31-45 odd)