Chapter 3: Functions and Graphs Section 3.1: The Coordinate Plane & Section 3.2: Relations and Functions

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Goal: To graph ordered pairs on a coordinate plane and to determine the coordinates of a point, given its graph. To determine the domain and range of relations and functions and to determine whether a relation is a function.

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Cartesian coordinate plane – composed of x-axis (horizontal) and y-axis (vertical) Meet at the origin (0, 0) Divide plane into 4 quadrants Ordered pair (x, y)

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Relation – set of ordered pairs Domain – set of all first coordinates (x) To determine a graph’s domain, look left to right Remember Rules: Can’t divide by zero and can’t take the square root of a negative number Range – set of all second coordinates (y) To determine a graph’s range, look bottom to top

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Function – special relation where each element of the domain is paired with exactly one element of the range Mapping shows how the members are paired One-to-one function – A function in which each element of the range is paired with exactly one element of the domain

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Write a rule for each relation and state the domain and range. 1. {(2, 4), (3, 6), (5, 10)} 2.{(4, 0), (1, -3), (-1, -5)}

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Vertical Line Test – determines if a graph is a function If no vertical line intersects a graph in more than one point, the graph represents a function If some vertical line intersects a graph in two or more points, the graph does not represent a function

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Example 1 State the domain and range of a relation shown. Is the relation a function? (-4,0) (-3, 1) (0, -2) (1, 2) (3, 3)

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Example 3 Graph y = 3x – 1 and find the domain and range. Then determine whether the equation is a function.

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Independent variable – values that make up the domain (usually x) Dependent variable – the other value (usually y) because it depends on x

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Homework: Pg. 101 #2-38 (even)

Sections 3.1 & 3.2: The Coordinate Plane & Relations and Functions Domain/Range Handouts of graphs Domain/Range Handout for function notation