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1.6 Relations and Functions

This guide dives into the concepts of relations and functions in mathematics, exploring essential questions like whether a student can have multiple telephone numbers or heights, and if one person's phone number can belong to another. It explains key vocabulary such as "relation," "domain," and "range," alongside the criteria that determine whether a relationship is a function. Practical examples including ordered pairs, the vertical line test, and function notation help illustrate these concepts, making it accessible for students learning about mathematical relationships.

justin-bullock
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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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