Function and their graphs ppt

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Function and their graphs ppt

  1. 1. MATH-001Dr. Farhana ShaheenTHE CARTESIANCOORDINATE SYSTEM
  2. 2. THE CARTESIAN COORDINATE SYSTEM We know that One dimensional numbers can be represented as points on a number line, and can be oriented either to the left (negative), or to the right (positive) of the origin (the zero point). Cartesian coordinates are just the natural extension of the number line into two (or three) dimensions. In the two dimensional case, we just use two number lines (or "axes"), called the x axis and y axis, at right angles to each other.
  3. 3. CARTESIAN PLANES AND COORDINATES
  4. 4. QUADRANTS IN CARTESIAN PLANES
  5. 5. QUADRANTS
  6. 6. POINTS IN CARTESIAN PLANE
  7. 7. LINEAR EQUATIONS
  8. 8. GRAPH OF LINEAR EQUATIONS Y = AX+B
  9. 9. PARABOLA
  10. 10. 2EQUATION OF PARABOLA y x 2Graph of y x
  11. 11. 2 y x y xGRAPH OF
  12. 12. DRAW THE PARABOLA
  13. 13. PARABOLAS WITH DIFFERENT SHAPES
  14. 14. PARABOLAS IN NATURE
  15. 15. PARABOLAS IN LIFE
  16. 16. PARABOLIC BUILDING
  17. 17. RELATIONS ARE SET OF ORDERED PAIRS
  18. 18. FUNCTIONSFunctions are relations, set of ordered pairs, in which the first elements are not repeated. For example: A= {(1, 3), (2, 5), (3, 4), (4, 7), (5, 2)}Note: B= {(1, 1), (2, -4), (2, 4), (3, 9), (3, -9)} is NOT a Function. (Why?)
  19. 19. FUNCTIONS ARE SET OF ORDERED PAIRSWHERE X-COORDINATE IS NOT REPEATEDCHECK FOR FUNCTIONS:
  20. 20. EXAMPLE OF A FUNCTION (Y CAN BE REPEATED)
  21. 21. DOMAIN AND RANGE OF A FUNCTIONTHE DOMAIN IS ALL THE X-VALUES, AND THERANGE IS ALL THE Y-VALUES.EXAMPLE: FIND THE DOMAIN AND RANGE.
  22. 22. DOMAIN AND RANGE OF A RELATION State the domain and range of the following relation. Is the relation a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} The above list of points, being a relationship between certain xs and certain ys, is a relation. Domain: {2, 3, 4, 6} Range: {–3, –1, 3, 6}
  23. 23. DOMAIN AND RANGE OF A FUNCTION
  24. 24. FUNCTIONS?
  25. 25. VERTICAL LINE TEST FOR GRAPH OF FUNCTIONS
  26. 26. CHECK FOR GRAPHS OF FUNCTIONS
  27. 27. GRAPHS OF FUNCTIONS?
  28. 28. EXAMPLE: The set A= {(1, 1), (2, -4), (2, 4), (3, 9), (3, -9)} is NOT a Function. These are the ordered pairs obtained fromthe equation 2y x y x
  29. 29. FUNCTION IS AN INPUT/OUTPUT MACHINE
  30. 30. FUNCTION IS AN INPUT/OUTPUT MACHINE
  31. 31. THANK YOU

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