Unit 2- Interpreting Functions

1. Unit 2- Interpreting Functions 2A- I can use technology to graph a function and analyze the graph to describe relevant key features (End Behavior, Domain, Range, Min/Max, x-& y- intercept)

2. Analyzing Graphs of Functions • Key Features of Graphs • Every type of function has its own unique set of key features which can include vertical and horizontal asymptotes as well as axis of symmetry • When analyzing ALLfunctions the key features include: • Domain • Range • End Behavior • Minimum(s) • Maximum(s) • X-Intercepts (roots) • Y-Intercept • Asymptotes • Axis of Symmetry

3. Can you Name the Function?

4. Examples • Given the function below list all the key features applicable. What type of function is this?

5. Examples • Given the function below list all the key features applicable. What type of function is this?

6. Examples • Given the function below list all the key features applicable. What type of function is this?

7. Functions Scavenger Hunt • With a partner • Must travel around the room together • Both complete the graphic organizer • Symbol & Fill in the blanks • Don’t give answers away to other groups • Symbols are on the top left • Should hear academic vocabulary (cubic, quadratic, maximum, x-intercept, …)

8. Exit Slip What are all the key features of the normal curve?

9. Unit 2- Interpreting Functions 2C- I can define a function and describe its Domain and Range graphically, algebraically and numerically and interpret the domain and range for a given situation

10. Unique Function • What function is he using to represent the situation he is describing? • What key features does his function have? • What is the Domain & Range of his function?

11. II. Domain and Range of Functions • Definitions • The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. • The range is the set of all possible output values (usually the variable y, or sometimes expressed as f(x)), which result from using a particular function • A function is a set of point in which all domains are paired with exactly one range (called one-to-one) • A relation is any set of points that is NOT one-to-one

12. B. Notation • Domain and range can be written: • Algebraically • Using Interval Notation • Described Verbally (graphically)

13. Examples • Algebra I-State the domain and range of the set of points below. Is the set of points a relation or a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

14. Examples • Algebra I-State the domain and range of the set of points below. Is the set of points a relation or a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} {(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

15. Examples • State the domain and range of the function. What type of function is this?

16. Examples • State the domain and range of the function. What type of function is this?

17. Examples • State the domain and range of the function. What type of function is this?

18. Examples • State the domain and range of the function. What type of function is this?

20. List all Key Features of the function given below (name the function). Square Root Function Y-Intercept: (0, 5) End Behavior: X + then y + Domain: All real numbers Range: y ≥ 5

21. If you Roll… • 0 Determine Domain and Range of the function and write in algebraic form • 1 Determine the End Behavior of the function • 2 Analyze the function for ALL key features • 3 Find any three key features of the function • 4 Determine Domain and Range of the function and write in interval notation • 5 Determine the End Behavior of the function

22. Homework Options

24. Graph Each Function and Analyze all Key Features Level A Level B Level C

25. Unit 2- Interpreting Functions 2D-I can describe relevant key features of piece-wise functions, explain how the constraints determine the domain, use the constraints to evaluate the function and graph linear piece-wise functions.

26. III. Piecewise Functions • In real life, most situations cannot be represented using only one function. • A piecewise function is a function that is defined on a sequence of intervals/domains • Examples • Define the domains in the piecewise function and explain what any key features represent.

27. The function below represents parking lot rates near UCLA during the week. Define the domains in the piecewise function and explain what any key features represent.

28. The function below represents Jessica’s climb to the top of a waterslide and then her decent. Define the domains in the piecewise function and explain what any key features represent.

29. Define the functions and their domains in the piecewise function below. What is the range of the function?

30. Define the functions and their domains in the piecewise function below. What is the range of the function?

31. Define the domains for this piecewise function • Identify the key features of this piecewise function

32. Together: • Create a story that goes with this function • What do the key features mean within the context of your story?

33. Galley Walk • Pink papers around the room • Level A-B-C • Answers on back; check your work & explanations

34. FYI-Upcoming… • Tutoring with DeVeny • Tuesday 7am • Thursday 7am • Afterschool tutoring • Mon-Thur 2:45-4:00 BAYLIS rm 607 • Test next week (T or W) • Unit 1 AND Unit 2

35. IV. Evaluating Functions • Reminder: All functions have a domain and a range. • Vocabulary: • Domain=x-values=input • Range=y-values=output • Evaluating a function is when a given input is placed into a function and the output is determined • Examples

36. Evaluate the function for the given inputs f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9 • g(-3)

37. Evaluate the function for the given inputs f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9 • h(4)

38. Evaluate the function for the given value of x • f(2)

39. Evaluate the function for the given value of x • m(-8)

40. Evaluate the function for the given value of x • m(10)

41. Evaluate the function for the given value of x • f(0)

42. Evaluate the function for the given inputs f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9 • x= -4

43. Sideways • Complete a problem • Find your answer • Can’t find it? Check for a mistake! • Move SIDEWAYS for a new problem

44. Error Analysis • What type of error (if any) did you make? • Mark exit ticket with type of error • Write sentence about what was missing/wrong • Log levels onto learning target logs

45. Quick Check The scores on the chapter 3 exam in Alex’s history class were normally distributed with a mean of 71 and a standard deviation of 5. Alex scored a 74. He knows that his parents will not be happy; thus, his plan is to use what he learned in Algebra II and explain to his parents that he scored higher than 60% of his class. Is Alex’s statement accurate? Explain why or why not.

46. Alex’s statement is not correct. He is getting the z-score associated with his test confused with the actual area under the normal curve. Z= Alex’s z-score is 0.60 but this does not mean that he scored better than 60% of his class. 0.60 is the z-score needed to look upthe percentage of students who scored lower than him using the z-table. A z-score of 0.60 gives an area of 0.7257; thus Alex actually scored higher than about 73% of the students in the class.

47. Homework Options

48. V. Graphing Linear Piecewise Functions • The domain is VERY important when graphing piecewise functions • Open circle the domain value is not included (not equal to) • Closed circle the domain value is included (equal to) • To graph a linear piecewise function graph each “piece” of the piecewise function and them apply the given domain to each linear function

49. Prior Knowledge Check (Algebra I) On Your OWN Graph… • y=8x-9 • -6x+4y=-36 • -10y=5x+20

50. Prior Knowledge Check (Algebra I) Together: What was your APPROACH to graphing each line? • y=8x-9 • -6x+4y=-36 • -10y=5x+20