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End Behavior Worksheet

Function Operations

Addition We can add two functions together. (f + g)(x) = f(x) + g(x)

Example For example: Let f(x) = 3x, g(x) = 2x + 1 (f + g)(x) = When you add, combine like terms!

You Try! Add f(x) + g(x) 1. f(x) = 4x + 3 and g(x) = 4 – x 2. f(x) = 5x + 1 and g(x) = 2x – 4

Subtraction (f – g)(x) =f(x) – g(x) Ex) Let f(x) = 5x and g(x) = x + 4 (f – g)(x) = When subtracting, distribute the negative!

You Try! 1. Find f(x) – g(x) f(x) = 8x + 4 and g(x) = 5x – 3 2. Find g(x) – f(x) f(x) = 3 – 2x and g(x) = -5x

Multiplication (f g)(x) = f(x)  g(x) Ex: Find (f g)(x) if f(x) = 3x + 1, g(x) = 2x

REMEMBER! Use the distributive property when multiplying two expressions with two terms! (3x + 1)(2x + 4)

You Try! Multiply: 1. f(x) = -x and g(x) = 2x + 1

Function Operations

Composition The composition of function f with function g: This is read “f composition g” and means to copy the f function down but where ever you see an x, substitute in the g function.

Find Let f(x) = 2x, g(x) = 3x + 1

Find Let f(x) = 2x – 3 and g(x) = 5x - 1

Composition Given the functions: f(x) = 5x and g(x) = x + 1 Find g(f(x)) f(g(x)) f(g(2)) g(g(x))

Composition of Functions Let f(x) = x -2 and g(x) = x2 . Find:

Composition of Functions Let f(x) = x -2 and g(x) = x2 . Find: