Drill #16 List the relation (set of ordered pairs) and the domain and range of the following mapping: Draw a mapping, and state the domain and range of the following relation: {(-3,1), (-2, 1), (3, 1)} x y

2-1 Relations and Functions Objective: To graph a relation, state its domain and range, and determine if it is a function, and to find values of functions for given elements in a domain.

Cartesian Coordinate Plane ** 1.Cartesian Coordinate Plane: Composed of an x-axis (horizontal) and y-axis (vertical) which meet at the origin and divide the plane into four quadrants. 2.x – axis: The horizontal axis in the coordinate plane. 3.y – axis: The vertical axis in the coordinate plane. 4.origin: The point where the x-axis meets the y-axis corresponding the coordinate (0,0)

The Coordinate Plane* Quadrant I ( +, + ) Quadrant II ( -, + ) Quadrant III ( -, - ) Quadrant IV ( +, - ) x-axis y-axis (0,0) Origin

Relations, Domain, and Range ** 5. relation: A set of ordered pairs. 6. domain: The set of all the x – coordinates (the 1 st numbers) of a relation. 7. range: The set of all the y – coordinates (the 2 nd numbers) of a relation. Example: For the relation {(-1, 2), (-1, 3), (-1, 4)} D = { -1 } R = { 2, 3, 4 }

Classwork 2-1 Study Guide #1-2

Mapping ** 8. mapping: Shows how each element of the domain is paired with each element of the range. Example: Mapping**: { (-1, 2), (-1, 3), (-1, 4) } X Y

The function machine… Suppose there is a function (machine) that takes numbers and transforms them… Consider the function f(x) that does this: f(0) = 0 f(1) = 2 f(2) = 4 f(3) = 6 What is the function? What does the graph of the function look like?

Functions ** 9.function: A special type of relation in which each element of the domain is paired with exactly one element of the range. NOTE : In a function, every x – value (input) has exactly one y – value (output). f(x) = y  f(1) = 2 corresponds with the ordered pair (1, 2).

Domain, Range, and Functions* Identify the domain and range of each mapping. State whether or not each is a function: Ex1:Ex2: 2 3 XY Y X 4

Vertical Line Test ** 10. Vertical Line Test: If a vertical line intersects a graph at more than one point then the relation is not a function. NOTE: Pass a pencil vertically over a graph. If the pencil ever touches more than one point at a time on the graph, then the graph fails the vertical line test, and is not a function. Every x – value must have a unique y –value.

Function? x y 1

Function? x y 1

Function? x y 1

Function? x y 1

Function? x y 1

Independent and Dependent ** 11.independent variable: the input of a function (x) 12.dependent variable: the output of a function (y) which depends on the value of the input. The value of the dependent variable (output) depends on the independent variable (input).

(13.) Discrete Function, (14.) Continuous Function** Discrete Function: A graph whose points are disconnected. Continuous Functions: A function whose graph is a line or a curve.

Graphing Functions: Find the missing values and plot the points Ex1. y = 3x – 4 Ex2. xy xy

Evaluating f(x)* Given the function Find: Ex1: f(0) Ex2: f(-2) Ex3: f(4a) Ex4: f(m – 1)

Study Guide Examples 2-1 Study Guide #3-8

Rewind A relation is a function if … The domain is … The range is … A continuous function is … discrete?

Homework 2-1 Practice (ALL)