Relations and Functions

Georgia Performance Standard (GPS): MM4A1

“Students Will Explore Rational Functions.”

A. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

B. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

GPS MM4A1

C. Solve rational equations and inequalities analytically, graphically, and by using

appropriate technology.

GPS MM4A1

What is a function and how do I recognize it?

EQ:

Relation: a set of ordered pairs – each x-value is paired with one or more y-values

Function: a set of ordered pairs, no x-value is repeated – each x-value is paired with exactly one y-value

Vertical Line Test: the graph of a relation represents a function if no vertical line intersects more than one point on the graph at the same time

Vocabulary

Domain – all x-values Range – all y-values

Continued…

Does { (1,3) (2,5) (3,4) (2,-6) } represent a function?

YES or NO? What is the domain? What is the range?

Example 1

Is the following a function?

Example 2

Function?

Example 3, 4, and 5

“Evaluate” means to solveEX. 6:Evaluate each function for the given values of

xf(x)=2x-3 for x=1 and x=-3

Evaluate

Pg. 107, #’s 5-10 and pg. 108, #’s 16-50 all

Assignment:

Answers5. No6. Yes7. Yes8. No9. Yes10. No16. Yes17. Yes18. No19. Yes20. Yes

21. Yes22. Yes23. Yes24. No25. No26. No27. Yes28. No29. Yes30. No31. Yes32. Nope

Answers continued…33. No34. Yes35. Yes36. No37. D: 0, 3 R: 2, 438. D: 1, 2, 3 R: 539. D: 7, 8, 9 R: -3, -2, -140. D: 4, 5, 6 R: 1, 2, 341. D: 4, 5, 6 R: -6, -5, -4

42. D: 0, 1.5, 2.5R: 043. -4; 044. 2; -445. -1; 1/346. -13/5; 147. 9; 2048. 3; 2.7549. 1/3; 3/1650. -9; -16