Introduction to Functions What’s New? Coordinate Plane, or System Domain and Range Not a Function At All! What is a Function? Students will need a copy of the Vocabulary Notes Cain Oct ‘08

A function is graphed on a coordinate plane, or system. Introduction to Functions Coordinate Plane, or Coordinate System A function is graphed on a coordinate plane, or system. 2-Dimensional Graphs Vertical axis (up and down) is the y-axis called the RISE Horizontal axis (left and right) is the x-axis called the RUN Where they intersect is the origin

(3,1) Coordinate Plane or Coordinate System 2-Dimensional Graphs Ordered Pairs give the placement of a point on a graph First number is the value on the x-axis Second value is the value on the y-axis (3,1) 1 3

What is the ordered pair naming the black point? Coordinate Plane or Coordinate System Domain and Range 2-Dimensional Graphs Ordered Pairs give the placement of a point on a graph What is the ordered pair naming the black point? (0,0) Where would (-2,3) be? 2. Where would (-3,0) be? 3. Where would (3,-3) be? 4. Where would (-1,-2) be?

Ordered Pairs give the placement of a point on a graph Domain and Range 2-Dimensional Graphs Ordered Pairs give the placement of a point on a graph A set of ordered pairs is a relation first value x-value is the Domain second value y-value is the Range {(-2,3), (-3,0), (3,-3), (-1,-2)} Domain is {-3, -2, -1, 3} What is the Range? What is the Domain? Range is {-3, -2, 0, 3}

Domain and Range {- 2 , 0, 2, 4} {- 3 , - 1, 1, 3} {- 5 , -2, 1, 4} What is the domain and range of the graph? {- 2 , 0, 2, 4} DOMAIN: RANGE: {- 3 , - 1, 1, 3} DOMAIN: What is the domain and range of the table? {- 5 , -2, 1, 4} x -5 -2 1 4 f(x) -1 RANGE: {- 2 , - 1, 0, 1}

Introduction to Functions What is a Function? A function is a relation in where each member of the domain is paired with exactly one member of the range. Each x-value is used once AND ONLY once. No x-value is repeated with a different value of y. x 1 2 3 f(x) -2 -1 x -5 -2 1 4 f(x) -1 Is this a function? YES NO

Not a Function At All! GRAPHS with points and lines To check whether a graph is a function, use the vertical line test. The vertical line test: if you can draw a vertical line anywhere and it touches 2 points or crosses a line twice, it is Not a Function At All! Are these 4 points a function? Is this black line a function? NO NO

Relations in Tables or Sets This is Not a Function At All! x 1 2 3 f(x) 4 Is each member of the domain paired with exactly one member of the range? This is Not a Function At All! {(-2,3), (-3,0), (3,-3), (-2,-2)} x = 1 is repeated with 2 values of y! This is Not a Function At All! x = -2 is repeated with 2 values of y!

What is a Function? GRAPHS with points and lines Using the vertical line test, are these points a function? YES Is the black line a function? YES

Relations in Tables or Sets What is a Function? Relations in Tables or Sets x 1 2 3 4 f(x) -3 -1 x 1 2 3 4 f(x) Is each member of the domain paired with exactly one member of the range? This is a Function! This is a Function! WAIT! Each value for the range (y) is 4! Does that matter? {(-4,3), (-3,2), (-2,1), (-1,0)} NO! Only the domain matters! This is a Function!

relation: a set of ordered pairs What is a Function? REVIEW A function is a relation in where each member of the domain is paired with exactly one member of the range. relation: a set of ordered pairs Each x-value is used once AND ONLY once. No x-value is repeated with a different value of y.