Function Notation 2.3 – Fun functions 2.3 Function Notation I can: Use Function Notation to evaluate function values.

(Not in your notes) Guess My Rule: What is this machine doing? 4 12 x + 2 -4 x + 2 10 -6 2 x x y 2 4 10 12 -6 -4 x x + 2

Guess My Rule: What is this machine doing? -50 15 5x 1 x 5x 1/5 -10 3 x y 3 15 -10 -50 1 1/5 x 5x

Guess My Rule: What is this machine doing? 21 -1 9 2x+1 10 -1 x 2x+1 4 x y 4 9 -1 -1 10 21 x 2x+1

Recall: x y Definition of a function: each __is paired with only one __ x is called the _________ y is called the _________ input Each input gives its own output output x y f Function Machine

x Function Notation: f(x) = 2x + 5 f(x) say “f of x” means the same thing as “y” y = 2x + 5 f(x) = 2x + 5 f(x) say “f of x” f(x) tells what to do with _____ You can use other letters for other “rules”. . . g(x), h(x), etc… x

Writing “stuff” in function notation Ex 1. Find f(3) Before: y = 2x + 5. Find y if x = 3 Now: If f(x) = 2x + 5, find f(3)

Ex 2. Suppose g(x) = 10 + ½ x. Find: = 10 – 2 = 10 + 5.5 = 8 = 15.5 g(-4) = 8 g(11) = 15.5

Your Turn: Suppose f(x) = –3x + 8. Find: f(4) f(–2) f(0) = 6 + 8 = –12 + 8 = 0 + 8 f(–2) = 14 f(0) = 8 f(4) = –4

Hmmm…with powers?? Ok! Example 3. Suppose f(x) = x2 – 5 Find… f(2) f(-1) f(-1) = (-1)2–5 f(2) = (2)2–5 = 1–5 = 4–5 POSITIVE 1! f(-1) = -4 f(2) = -1

A cubed?? NO WAY! Example 4. Suppose j(x) = x3 + 1 Find… j(3) f(3) = (3)3+1 = 27 + 1 f(3) = 28

Are you a Master? = 3(–5)2 + (–5) – 1 = 3(25) + (–5) – 1 = 75 – 5 – 1 If f(x) = 3x2 + x – 1, then find f(-5).   = 3(–5)2 + (–5) – 1 = 3(25) + (–5) – 1 = 75 – 5 – 1 = 69

Vocab filler Function Notation