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Relations and Functions

Relations and Functions. 8.1. Relation. A set of ordered pairs Example: { (1,2), (0,-4), (3,8)}. Domain. The first coordinates of the relation X-value Example: What is the Domain of : { (1,2), (0,-4), (3,8)} 1,0,3. Range. The second coordinates of a relation Y-value

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Relations and Functions

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  1. Relations and Functions 8.1

  2. Relation • A set of ordered pairs • Example: { (1,2), (0,-4), (3,8)}

  3. Domain • The first coordinates of the relation • X-value • Example: What is the Domain of : { (1,2), (0,-4), (3,8)} 1,0,3

  4. Range • The second coordinates of a relation • Y-value • Example: What is the Range of: { (1,2), (0,-4), (3,8)} 2,-4,8

  5. Function • Some relations are functions • A function is one to one. • Each member of the domain is paired with exactly one member of the range. • One x to on y • X-values can not repeat to different Y’s • Y-Values CAN repeat

  6. Math =Love Mathematical Dating Advice for Functions: Is this a function: (Juan Pablo, Nikki) (Juan Pablo, Claire) No!!! As you can see Juan Pablo is dating both Nikki and Claire therefore this is not a functional relationship

  7. Is this relation a function? {(0,1), (1,2), (1,3), (2,4)} List the domain and range values in order and draw arrows from the domain to the range to determine. Domain Range 0 1 • 2 • 3 4 No, because 1 goes to 2 and 3

  8. Determine if each relation is a function 1.) {(-2,3), (2,2), (2,-2)} 2.) {(-5,-4), (0,-4), (5,-4)}

  9. Examples: Tell if the Graph is a function NOT a function

  10. Graphing Relations and Functions • A relation is a set of ordered pairs. • Ordered pairs can always be graphed on a coordinate plane

  11. Vertical Line Test • Used to determine if a graph is a function • How: Draw vertical lines over the graph • To determine a pass or fail: • Pass of the VLT (The graph is a function) : The vertical lines only cross the graph once • Fail of the LT (The graph is not a function): The vertical lines cross the graph twice or more.

  12. Is this a graph of a function? Vertical Line Test

  13. Is this a graph of a function?

  14. Is this a graph of a function?

  15. Is this a graph of a function?

  16. Is this a graph of a function?

  17. Is this a graph of a function?

  18. Graph the relation and then use the Vertical Line Test to determine if the relation is a function

  19. Homework Page 389 (12-23) all

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