Precalc 8.19.13

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Precalc 8.19.13

  1. 1. New seating chart today 2 3 1 4
  2. 2. The Lame Joke of the day.. What did the traffic light say to the car? And now it’s time for.. Don’t look I’m changing!
  3. 3. Don’t forget! • Problem of the week can be done for extra credit. • See the bulletin board in class, or the discussion board on echo.
  4. 4. Functions • Definitions • Examples • Graphs • Vocabulary • Symbols and notation
  5. 5. Relation • Pairs of quantities that are RELATED in some way.
  6. 6. Vocabulary • Function: A special type of Relation in which each input value (Domain) is matchup up with exactly one output value (Range). Usually we describe a function with an equation.
  7. 7. Grading Function
  8. 8. Vocabulary • Function: Rule that assigns each input value to exactly one output. Usually we describe a function with an equation. • Domain: x –values, or input values. • Range: y – values , or output values.
  9. 9. How do we know if a graph is a function? • If it passes THE VERTICAL LINE TEST The vertical line test 1. Move a vertical line across the entire graph from left to right. 2. If it intersects the graph only ONCE in all locations, then it is a function.
  10. 10. Is this a function?
  11. 11. Is this a function?
  12. 12. Is this a function?
  13. 13. What is the Domain and Range?
  14. 14. What is the Domain and Range?
  15. 15. What is the Domain and Range?
  16. 16. Function notation )(xf Whatever is in the parentheses gets plugged into the function.
  17. 17. Practice 1. Is a function represented? If so what is the domain and range. a. (2,-4) (4,4) (6,-1) (5,0) (1,6) (2,4) (3, -2) b. 2. If , then find f (0) , f (-2) , and f (3a)5)( 2 xxf
  18. 18. Finding the domain from the equation Example: What is the domain of the function given by Functions only have real number outputs. Anything that gives an imaginary number or a zero denominator is a restriction. How to find the domain: Assume that the domain is the set of all real numbers except for the restrictions. 5)( xxf
  19. 19. Examples • What is the domain? • What is the domain? 7 2 )( x xf 9 7 )( 2 x xf
  20. 20. More challenging examples • What is the domain? • What is the domain? 4 32 )( xx xf 6 9 )( x x xf
  21. 21. Practice • What is the domain? • What is the domain? • What is the domain? xx xf 5 5 )( 2 7)( 2 xxf 3 7)( xxf
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