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Pre-Cal 20S January 12, 2009

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Introduction to functions: functions vrs relations, domain, and range.

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Pre-Cal 20S January 12, 2009

  1. 1. Functions 2222 holes by flickr user jared
  2. 2. What is a function? Let's play a game ... All functions are relations, but not all relations are functions.
  3. 3. Relations x 2+ y 2= 25 one-to-many Functions one-to-one many-to-one y=x-2 y = x2
  4. 4. Relations x 2+ y 2= 25 one-to-many Functions one-to-one many-to-one y=x-2 y = x2
  5. 5. Domain & Range of a Function Symbolically y=x-2 1 -2 mapping 4 5 9 -2 Graphically output input range domain Numerically {(1, -2), (4, 5), (9, -2)}
  6. 6. R D Functions or Relations? write as ordered pairs 2 2 -1 -1 -3 -4 5 3 R R D D 6 -1 2 2 -4 8 -3 -4 R D D R
  7. 7. Domain & Range of a Function Domain: Range:
  8. 8. Functions or Relations? relation function Identify the domain and range of each. relation DOMAIN (3, 2), (2, 3), (3, 3) RANGE function (1, 4), (4, 1), (-1, 4) DOMAIN RANGE relation (-5, 2), (0, 2), (-5, 3) DOMAIN RANGE function (5, -2), (3, 2), (6, 2) DOMAIN RANGE
  9. 9. Example 1 An example of a relation, that is a function is: x y -2 -4 y=x-2 -1 -3 0 -2 1 -1 2 0 An example of a relation, that is NOT a function is: xy -3 -4 x 2 + y 2= 25 -3 4 0 -5 05 43 What's The Verticle Line Test?
  10. 10. The Verticle Line Test Sweep a vertical line across the graph of the function. If the line crosses the graph more than y = x2 once it is not a function, only a relation.
  11. 11. HOMEWORK Exercise #48 & #49

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