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1.6 Relations and Functions

1.6 Relations and Functions. Appetizers. Can a student have more than one telephone number? Can a student have more than one height? Can a phone number belong to more than one person?. Some Vocabulary so we all speak the same language.

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1.6 Relations and Functions

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  1. 1.6 Relations and Functions

  2. Appetizers . . . Can a student have more than one telephone number? Can a student have more than one height? Can a phone number belong to more than one person?

  3. Some Vocabulary so we all speak the same language . . . relation: a pairing of input values with output values, such as an ordered pair. For any (x, y), x is the input and y is the output. domain: set of input values for a relation. range: set of output values for a relation.

  4. 123456 9 13 15 12 10 12 Table Graph Mapping Diagram Ordered Pairs {(1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)} domain(input) range(output)

  5. Function or not a function?That is the question! function: there is only one output for each input, so each element of the domain is mapped to exactly one element in the range. Huh? No repeats for x. Repeats on y are OK. A B C A B C 2 2 Function NOT a function {2, A), (2, B), (2, C)} 2 is used more than once {A, 2), (B, 2), (C, 2)} 2 is used more than once

  6. -2 -1 0 1 2 5 6 7 8 Function or not a function?That is the question! Press Function or NOT a Function, then explain. X NOT a Function Function

  7. -2 -1 0 1 2 3 4 5 Function or not a function?That is the question! Press Function or NOT a Function, then explain. X Function NOT a Function

  8. Function or not a function?That is the question! Press Function or NOT a Function, then explain. X NOT a Function Function

  9. Function or not a function?That is the question! Press Function or NOT a Function, then explain. X Function NOT a Function

  10. Function or not a function?That is the question! Press Function or NOT a Function, then explain. {(1, 0), (2, –1), (3, 0), (3, –1), (4, 0)} X Function NOT a Function

  11. Function or not a function?That is the question! Press Function or NOT a Function, then explain. {(1, 0), (2, –1), (3, 0), (4, –1)} X NOT a Function Function

  12. What about graphs? Vertical line test (VLT): If any vertical line passes through more than one point on the graph of a relation the relation is not a function. Function

  13. VLT, cont. Not a Function

  14. VLT, cont. Function Not a Function

  15. VLT, cont. Function Not a Function

  16. VLT, cont. Function Not a Function

  17. VLT, cont. Function Not a Function

  18. VLT, cont. Function Not a Function

  19. VLT, cont. Function Not a Function

  20. Finding Domain and Range from a Graph Range = [0, 2] Domain = [-2, 2]

  21. Helicopter taking off, hovering briefly, then landing.

  22. Speeding baseball being caught by an outfielder.

  23. Helicopter taking off, hovering briefly, then landing.

  24. 1.7 Function Notation

  25. y is now f(x) function function notation Find y when x=-3; or evaluate the function when x=-3

  26. Any letter goes! function function notation

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