Warm- UP

F(x) = x + 2, g(x) = -x + 3

1. Add the two functions2. Subtract the two functions3. 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) = x2 + 2x – 1 Find (f+g) (x) when x = 2 (f + g) (x) = f(x) + g(x) = 2x + 1 + x2 + 2x – 1 = x2 + 4xNow plug in 2(2)2 + 4(2) = 4 + 8 = 12

Finding the difference of two functions

If f(x) = 2x + 1 , and g(x) = x2 + 2x – 1Find (f – g)(x) when x = 2(f – g) (x) = f(x) – g(x) = 2x + 1 – (x2 + 2x – 1) = 2x + 1 - x2 - 2x + 1= - x2 + 2Now plug in 2-(2)2 + 2 = -4 + 2 = -2

Finding the Product of two functions

Given f(x) = x2 and g(x) = x – 3Find fg(x) when x = 4fg(x) = f(x) g(x) = (x2) (x-3) = x3 – 3x2

Now plug in 4(4)3 – 3(4)2 = 16

Finding the quotient of two functions

Given f(x) = √(x) and g(x) = √(4-x2). Find f/g(x) f/g (x) = f(x) / g(x) = √(x) / √(4-x2)

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-x2

1. Find (f◦g)(x) when x = 2

2. Find (g◦f) (x) when x = 1

Another Example

• Given f(x) = x2 – 9 and g(x) = √(9-x2) • Find (f◦g)(x)