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Introduction to Functions

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. Introduction to Functions. A function is graphed on a coordinate plane, or system.

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Introduction to Functions

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  1. 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

  2. Introduction to Functions A function is graphed on a coordinate plane, or system. Coordinate Plane, or Coordinate 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 3 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)

  4. What is the ordered pair naming the black point? Domain and Range Coordinate Plane or Coordinate System • 2-Dimensional Graphs • Ordered Pairs give the placement of a point on a graph (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?

  5. A set of ordered pairs is a relation What is the Domain? What is the Range? Domain and Range 2-Dimensional Graphs Ordered Pairs give the placement of a point on a graph 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} Range is {-3, -2, 0, 3}

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

  7. 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. once AND ONLY once. Each x-value is used No x-value is repeated with a different value of y. Is this a function? YES NO

  8. 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

  9. x = 1 is repeated with 2 values of y! x = -2 is repeated with 2 values of y! Not a Function At All! Relations in Tables or Sets 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)} This is Not a Function At All!

  10. 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

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

  12. 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 once AND ONLY once. Each x-value is used No x-value is repeated with a different value of y.

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