Bellwork Write the inequality for each graph:

Intro to Functions 2.3

Definition: Relation Relation: Each value of the 1 st variable (typically x) is paired with one or more values of the 2 nd variable (typically y). 2.3 Introduction to Functions A relation is a set of ordered pairs

Definition: Function Each value of the 1st variable (x) is paired with exactly one value of the 2nd variable (y). Trick: Do the x’s repeat? If so, then it is NOT a function!

Definitions: Domain & Range Domain (x): The set of all possible values for the first variable. Range (y): The set of all possible values for the second variable.

Example 1 State the domain and range of a relation, and state whether it is a function. { (–7, 5), (4, 12), (8, 23), (16, 8) } domain: { –7, 4, 8, 16} range: { 5, 8, 12, 23 } This is a function because each x-coordinate is paired with only one y-coordinate. 2.3 Introduction to Functions

Example 2 State the domain and range of the relation. Is this relation a function?

Question: What would a graph of a function have to look like?

Vertical Line Test (VLT) If every vertical line intersects a graph only once, then the graph represents a function. 2.3 Introduction to Functions functionnot a function

Example 2 What is the domain and range of this relation? Is this relation also a function?

Example 2 What is the domain and range of this relation? Is this relation also a function?

Example 2 What is the domain and range of this relation? Is this relation also a function?

Example 2 What is the domain and range of this relation? Is this relation also a function?

Homework Section Page all (31-36 draw graphs and show the vertical line test)

Bellwork 1. Classify the number: 2. Identify the domain and range:

Function Notation In the past we wrote: y = 3x + 4 Now we write: f(x) = 3x + 4 y is the same thing as f(x)

f(x) works the same way as an equation Graph: What is the product of the slope and y-intercept of

We can also use function notation to substitute values into an equation: In the past we wrote: y = 3x + 4 Find y if x = -3 Now we write: f(x) = 3x + 4 f(-3) =

Example 3 Given g(x) = 2x 2 – 3x, find g(-2). Given h(x) = 3 - x 2 find h(-5).

Homework Review Worksheet Quiz tomorrow on