1. Tuesday

2. Parent Function Quiz 4 Graphs No Calculators/No Notes Use entire 10x10 grid Don’t forget to graph asymptotes if needed! About 8-10 minutes to complete

3. Homework Questions?

4. Relations and Functions Chapter 2 Section 2-1 Pages 72-81

5. Objectives I can determine if the relation is a function by two methods. I can find Domain and Range from relations and continuous graphs IMPORTANT VOCABULARY in this section!!

6. Important Vocabulary Relation Domain Range Discrete Function Continuous Function Vertical Line Test

7. Quadrant I (+, +) Quadrant II (-, +) Quadrant IV (+, -) Quadrant III (-, -) Origin (0,0)

8. Relation A relation is a set of ordered pairs! Need the braces { } to show a set Example: { (1, 2), (3, 4), (5, 6) }

9. Domain and Range The domain in any relation is the first coordinates from the ordered pairs. It is the Input! Domain = X -Values The range in any relation is the second coordinates from the ordered pairs. It is the Output! Range = Y- Values

10. Dependent Variable

11. Example 1: Domain/Range Given the following relation {(2,3), (-4,8), (2,6), (7,-3)} What is the Domain? { -4, 2, 7} **Notice they are listed least to greatest!! No duplicates!!! What is the Range? {-3, 3, 6, 8}

12. Example 2: Given the following ordered pairs, find the domain and range. {(4,5), (-2,3), (5,6)} Domain is {-2, 4, 5} Range is {3, 5, 6}

13. Answer Format When listing a set of numbers for domain or range, use the set symbols {} List numbers from least to greatest (increasing order). No duplicates! Ex: the domain has numbers: 3, -2, 5, 2, 3 {-2, 2, 3, 5}

14. 4 Ways to see Relations

15. Relations Ordered Pairs {(2, 3),(-3, 1),(1, -2)} XY 23 -31 1-2 Data Tables Graphs Mapping 2 -3 1 3 1 -2 XY

16. Function A function is a special relation in which NO DUPLICATED “x-values” Example: Is the following relation a function: { (1,3), (4,-9), (6,3) } Answer: Yes. No x-values are duplicated

17. Ex 2: How about this relation. Is it a function? Given the following { (2,3), (-4,8), (2,6), (7,-3)} Function: No. The x-value “2” is duplicated

18. Tell whether the pairing is a function. Identify a function EXAMPLE 2 a. a. NOT a function because the input “0” is paired with both 2 and 3.

19. b.b. Identify a function EXAMPLE 2 Output Input 21 00 4 8 612 Function? Yes

20. GUIDED PRACTICE for Example 2 Tell whether the pairing is a function. 1221 Output 12963 Input 2. Function? Yes

21. GUIDED PRACTICE for Example 2 Tell whether the pairing is a function. 3210 Output 7422 Input 3. Function? No

22. Vertical Line Test You can use a vertical line test to easily see on a graph is the relation is a function. You place a straight edge like a pencil vertical on the graph and move it across the graph. If the line intersects the graph at only one point at a time, then it is a function.

23. Applying VLT

24. y 2 = x x y Vertical Line Test Consider the graphs. x 2 + y 2 = 1 x y y = x 2 x y 2 points of intersection 1 point of intersection 2 points of intersection Vertical Line Test

25. Discrete Function A function with ordered pairs that are just points and not connected.

26. Discrete Function

27. Continuous Functions?? A function is continuous if it has an infinite domain and forms a smooth line or curve Simply put: It has NO BREAKS!!! You should be able to trace it with your pencil from left to right without picking up your pencil 27

28. x y 4 -4 The domain of a continuous function is all x-values! We read domain from LEFT to RIGHT The range of a continuous function is all the y-values! We read range from BOTTOM to TOP. Domain Range Domain & Range

29. x y – 1 1 Example: Find the domain and range of the function f (x) = from its graph. The domain is [–3,∞). The range is [0,∞). Range Domain Example: Domain & Range (–3, 0)

31. Example 1

32. Example 2

33. Example 3

38. What Graph Activity Graphs A – Q around the room. Answer questions based on domain and range.

39. Homework WS 1-4 Quiz Next Class