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Math 9 Lesson #17 – Functions and Relations Mrs. Goodman

Math 9 Lesson #17 – Functions and Relations Mrs. Goodman. What is a relation ?. a mapping or pairing of input values with output values. A relation between two variables x and y is a set of ordered pairs (x, y). What is a function ?.

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Math 9 Lesson #17 – Functions and Relations Mrs. Goodman

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  1. Math 9 Lesson #17 – Functions and Relations Mrs. Goodman

  2. What is a relation? • a mapping or pairing of input values with output values. A relation between two variables x and y is a set of ordered pairs (x, y).

  3. What is a function? • A relation that has EXACTLY one output for every input.

  4. Answer the following questions about the three vending machines. • When a student pushes button number 3 on Machine B, what is the output • Coke

  5. If a student received a Sprite from Machine A, what was the input? • 2 • So, what represents the “input” of the vending machines? • Buttons

  6. What represents the “output?” • Soda • 5. One of the machines would not make a very good one. Which one is that and why?

  7. 6. Two of the machines above fit the definition of a function. Which two machines can be considered functions? Explain...

  8. 7. One machine does not fit the definition of a function. Which one is it and why?

  9. Venn Diagram: • All functions are relations.Not all relations are functions. Relations Functions

  10. Is the following a relation or a function?

  11. Is the following a relation or a function? • { (2, 3), (5, 4), (9, 1), (-3, 5) }

  12. Is the following a relation or a function? • { (-9, 10), (- ½ , -6), (8, 2), (-9, 1), (7, 17)}

  13. Is the following a relation or a function?

  14. Is the following a relation or a function?

  15. Is the following a relation or a function?

  16. Function Notation • f(x) • “f of x”

  17. f(x) = 3x – 4 • Find f(-2) • f(-2) = 3(-2) – 4 • = -6 – 4 • f(-2) = -10

  18. Find f(-5) for each function: • f(x) = 2x2 – 5x + 10 • f(x) = 3x – 10 • f(x) = 2x3 • f(x) = (x + 7)(2x – 1)

  19. That’s all for today! • Thanks for working hard. See you next time!

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