Functions
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Functions

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Functions Presentation Transcript

  • 1. Functions
  • 2. Analytic plane x-axis y-axis origin 1 st quadrant (+,+) 2 nd quadrant (-,+) 3 rd quadrant (-,-) 4 th quadrant (+,-)
  • 3. Ordered Pair:
    • Given that a and b are any two elements, (a,b) is called an ordered pair where a is first component and b is second component.
  • 4. Example:
    • ( 5 , -1)
    • ( abu , elham)
    • ( a , b)
    • ( square , triangle)
    • ( adhaser , 165 cm)
    • ( emanuel , ?)
  • 5. Example:
    • y = x – 2. Give four example for the ordered pair (x, y).
  • 6. Equality of ordered pairs
    • Let (m, n) and (p, q) be two ordered pairs.
    • (m, n) = (p, q) if and only if m = p and n = q.
    • Example: find x and y if (x + 1, 6) = (8, 2y – 4)
  • 7. Notations of intervals:
    • Let a and b be real numbers.
    A = [a, b] denotes the set of all real numbers between a and b (a and b are included). a b
  • 8. a b A = (a, b) denotes the set of all real numbers between a and b (a and b are excluded). A = [a, b) denotes the set of all real numbers between a and b (a is included and b is excluded). a b
  • 9. a b A = (a, b] denotes the set of all real numbers between a and b (a is excluded and b is included).
  • 10.