Warm-Up

7.6 Function Operations

With your table, try to extend what you know about adding and subtracting two functions and apply your knowledge to the following problem. How might we solve this? If f(x) = 2x2 + 3x + 10 and g(x) = 3x – 2, then evaluate (f × g)(2).

Review: What is a function? A relationship where every domain (x value has exactly one unique range (y value). Sometimes we talk about a FUNCTION MACHINE, where a rule is applied to each input of x

Function Operations

Adding and Subtracting Functions

Multiplying Functions

Dividing Functions

Let’s Try Some

Let’s Try Some

Let’s Try Some

Let’s Try Some

Function Composition Notation This does not say “FOG” You read this “f composed with g of x”

Function Composition Notation Another way to write this is OR f[g(x)]

Function Composition Notation

Function Composition EX 1: f(x) = x2 g(x) = x + 1 OR EX 1: f(x) = x2 g(x) = x + 1 Start with g(x) and put that in to f(x) = (x + 1)2 = x2 + 2x + 1

Function Composition EX 2: f(x) = x + 2 g(x) = 4 – x2 Start with g(x) and put that in to f(x) = (4 – x2) + 2 = -x2 + 6

Function Composition EX 3: f(x) = x2 + 1 g(x) = 2x Start with g(x) and put that in to f(x) = (2x)2 + 1 = 4x2 + 1

evaluating with Function Composition (Numbers) EX 4: f(x) = x2 + 1 g(x) = 2x Start with g(x) & find g(3). Put that answer in to f(x). g(3) = 6 f(6) = 37

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