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P.O. I can compare two functions represented in different ways.

P.O. I can compare two functions represented in different ways. L.O. I can define relation and function. I can determine whether a relation represented in different ways is a function.

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P.O. I can compare two functions represented in different ways.

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  1. P.O. I can compare two functions represented in different ways. L.O. I can define relation and function. I can determine whether a relation represented in different ways is a function. E.Q. What is a function? How do you identify a function? What are some ways in which you can represent functions?

  2. Motivate You and your friends are going to a basketball game. What is the relation between the total cost for tickets and the number of people in your group? Total cost is equal to the individual ticket price multiplied by the number of people in the group.

  3. Vocabulary: Relation A set of ordered pairs represented as (x,y). (0,3); (6,5); (3,7) Domain The set of x-coordinates of the ordered pairs. 0, 6, 3 Range The set of y-coordinates. 3, 5, 7

  4. Find the domain and range from the table below

  5. What is another name for Domain and Range?

  6. Vocabulary: A relation in which no two ordered pairs have the same x-coordinate. Function This relation is a function: (0,10), (1,2), (2,3) Example This relation is not a function: (1,1), (1,2), (2,3)

  7. What is a Function??? Examples Non Examples (3,90), (4,54), (6,71) (13,14), (13,5) , (16,7) (3,4), (4,5), (6,7), (3,9) (-1,2), (-4,51), (1,2) (8, 11), (34,5), (6,17), (8,19) (3,4), (4,5), (6,7), (1, 2)

  8. What is a Function??? Examples Non Examples (3,90), (4,54), (6,71) (13,14), (13,5) , (16,7) (-1,2), (-4,51), (1,2) (3,4), (4,5), (6,7), (3,9) (3,4), (4,5), (6,7), (1, 2) (8, 11), (34,5), (6,17), (8,19)

  9. Guided practice Is this a function? Explain your answer. 1. (6,1), (4,2), (6,-3),(2,5) 2. (5,8), (3,-2), (-2,-5),(0,0) 3. (2,4), (2,5), (2,6),(2,7)

  10. 1. ordered pairs- (1,0), (2,0), (3,3) 2. contextual situations 3. inputs and outputs- 4. graphs- Representations of functions.... 5. Equations

  11. Create a mapping from the set of ordered pairs. Is it a function? a) (5,8), (11,9), (6,8), (8,5) b) (3,4), (9,8), (3,7), (4,20)

  12. Input and Outputs State the domain and the range for each relation. Then, determine which relations represent functions. If the relation is not a function, state why not.

  13. Think Is it easier to determine if a relation is a function by viewing a mapping, a set of ordered pairs, or a table?

  14. Analyzing Contexts Example: Read each context and decide whether it fits the definition of a function. Explain your reasoning. 1. a) Input: Sue writes a thank-you note to her best friend. b) Output: Her best friend receives the thank- you note in the mail. 2. a) Input: A football game is being telecast. b) Output: It appears on televisions in millions of homes.

  15. Read each context and decide whether it fits the definition of a function. Explain your reasoning. 1. a) Input: The basketball team has numbered uniforms. b) Output: Each player wears a uniform with her assigned number. 2. a) Input: Tim sends a text message to everyone in her contact list. b) Output: There are 41 friends and family on Tim’s contact list. 3. a) Input: A sneak preview of a new movie is being shown in a local theater. b) Output: 65 people are in the audience

  16. Did you know? Functions can also be represented using an equation!!!

  17. Analyzing equations y = 3x To test whether this equation is a function, first substitute values for x into the equation, and then determine if any x-value can be mapped to more than one y-value.

  18. Guided Practice Determine whether each equation is a function. List three ordered pairs that are solutions to each. Explain your reasoning. a) y = 5x+ 3 b) y = x2 c) y = x

  19. Vertical line test You can determine whether a graph represents a function by using the vertical line test. If any vertical line intersects a graph at more than one point, the graph does not represent a function. Otherwise, the graph does represent a function.

  20. Not a function!

  21. Think and Discuss Does the graph above represent a function? Explain

  22. Think and Discuss Does the graph above represent a function? Explain

  23. Think and Discuss • Is this a linear function or a non-linear function?

  24. Ticket out • A relation is (always, sometimes, never) a function. • A function is (always, never) a relation

  25. Homework 1. Create a mapping that is a function. 2. Draw a graph that is not a function 3. Create a table that is a function 4. Create your own context problem, and decide whether it represents a function.

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