Warm- UP F(x) = x + 2, g(x) = -x Add the two functions 2.Subtract the two functions 3.Multiply the two functions

Math IV Lesson 4 Essential Question: How do you combine two functions to form another function Section objectives: Students will learn how to find the sum, difference, product, quotient, and composition of two functions. Standards : MM4A4. Students will investigate functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

1.5 Combinations of Functions Sum of functions (f + g) (x) = f(x) + g(x) Difference of functions (f – g) (x) = f(x) – g(x) Product of functions Fg(x) = f(x) g(x)

Finding the sum of 2 functions If f(x) = 2x + 1, and g(x) = x 2 + 2x – 1 Find (f+g) (x) when x = 2 (f + g) (x) = f(x) + g(x) = 2x x 2 + 2x – 1 = x 2 + 4x Now plug in 2 (2) 2 + 4(2) = = 12

Finding the difference of two functions If f(x) = 2x + 1, and g(x) = x 2 + 2x – 1 Find (f – g)(x) when x = 2 (f – g) (x) = f(x) – g(x) = 2x + 1 – (x 2 + 2x – 1) = 2x x 2 - 2x + 1 = - x Now plug in 2 -(2) = = -2

Finding the Product of two functions Given f(x) = x 2 and g(x) = x – 3 Find fg(x) when x = 4 fg(x) = f(x) g(x) = (x 2 ) (x-3) = x 3 – 3x 2 Now plug in 4 (4) 3 – 3(4) 2 = 16

Finding the quotient of two functions Given f(x) = √(x) and g(x) = √(4-x 2 ). Find f/g(x) f/g (x) = f(x) / g(x) = √(x) / √(4-x 2 )

Compositions of functions The composition of the function f with the function g is (f ◦ g) (x) = f(g(x)) Here you plug one function into another function. Always plug the right function into the left.

Examples Given f(x) = x + 2, and g(x) = 4-x 2 1.Find (f◦g)(x) when x = 2 2. Find (g◦f) (x) when x = 1

Another Example Given f(x) = x 2 – 9 and g(x) = √(9-x 2 ) Find (f◦g)(x)