1. Warm-Up: December 5, 2014 Input -2 -1 2 3 5 Output 1 6 22
A number is inputted into a magic box, which then outputs a different number.
Using the table below, what does the magic box do to the input number to get the output number?
Input -2 -1 2 3 5
Output 1 6 22

2. Investigation 5A Advanced Integrated Math I
Functions – The Basics
Investigation 5A
Advanced Integrated Math I

3. Goal for Today
Practice finding the rule to describe a set of input and output values.

4. Game Time Mr. Szwast will think of a rule.
You will tell Mr. Szwast the input, and then he will tell you the output. You then get to guess what the rule is.

5. Your Turn!
You will work with your partner. One person will be the Rule Maker, the other will be the Rule Guesser.
The Rule Maker must decide on a rule (simple enough that they can do the calculations in their head).
The Rule Guesser gives an input number to the Rule Maker. The Rule Maker gives the output value.
The Rule Guesser tries to guess the rule. Your score is the sum of the number of input values used and the number of rule guesses.
Switch roles with your partner and repeat.
Low score wins!

6. Assignment
Read pages
Page 364 #7-10

9. Warm-Up: December 8, 2014
Pick up a handout: “5.02 – Building Functions”
Read the front page and complete the table with your partner.
You may use a calculator.
Finish reading the rest of the handout.
Complete #2

10. Homework Questions?

11. Tables on TI-83/TI-84

12. You-Trys (with partner)
Use Sasha and Tony’s rule from the handout. Find the total costs of CD’s priced between $15 and $20. Use price increments of $1.
Describe any patterns in the table.
Find a simpler rule than Tony and Sasha’s rule that agrees with the table.
Tony and Sasha pay 5% sales tax whether they buy CD’s at the mall or the music store web site. Assume that the nondiscounted price of each CD is exactly the same at the mall and at the music store web site.
At what price is it a better deal to buy a CD at the music store web site? At the mall?
At what price is the final cost of a CD the same at the music store web site and at the mall?

13. Assignment
Page 370 #6, 7, 8, 12, 14

14. Page 370
See textbook for #8 and #14.

16. Warm-Up: December 9, 2014
Tony and Sasha are playing the Guess My Rule game.
In round 1, Tony is the Rule Maker.
When Tony uses a fair rule, what is the value of c?
How are the variables a and b related?
Do you have enough information to find the value of a?
Sasha’s Input
Tony’s Output 1
1 returns a 2
2 returns 7 5
5 returns 11
1 returns b
2 returns c

17. Homework Questions

18. Think-Pair-Share Tony and Sasha are playing the Guess My Rule game.
In round 2, Sasha is the Rule Maker.
Tony says, “That rule’s not fair!” What makes Tony say that?
Tony’s Input
Sasha’s Output 1
1 produces 5 2
2 produces 3 3
3 produces 25
1 produces 11

19. Section 5.03 Advanced Integrated Math I
Is It a Function?
Section 5.03
Advanced Integrated Math I

20. Essential Question
How can we determine if a relationship is a function?

21. The Function Machine

22. Add 2 to the input…

23. An Unfair Rule Add 2 or 3 depending on a coin flip

24. Functions
A function is a rule that assigns each input to exactly one output.

25. Think-Pair-Share
Does the rule “Add 4 to the input and square the result” define a function?

26. Think-Pair-Share
Does the rule “Find a number that is less than the input” define a function?

27. You-Try (with partner)
Give three examples of rules that define functions and three examples of rules that do not define functions.

28. Assignment
Read pages
Page 376 #5-9, 12

29. Page 376

31. Warm-Up: December 10, 2014 What is the input?
What is the name of the function?
What is the output?
What would the output be if the input were 3?

32. Homework Questions?

33. District Benchmark Tomorrow
Covers Chapters 1-3

34. Section 5.04 Advanced Integrated Math I
Naming Functions
Section 5.04
Advanced Integrated Math I

35. Essential Question
How do we evaluate functions and compositions of functions?

36. You-Try
The function f is defined by
Evaluate each of the following

37. Function Names We can give a function any name we want.
We can use transformation notation or function notation to write a function.

38. Compositions of Functions
We can take the output of one function, and make it the input of another function. This is called the composition of functions.

39. Example: Find f(g(5))

40. Example: Find g(f(5))

41. Assignment
Read pages
Page 381 #6-12

42. Page 381

44. December 11, 2014 District Benchmark Assessment
Have your page 376 assignment out for Mr. Szwast to check.
After your homework is checked, clear everything off of your desk except pencils, erasers, and a non-graphing calculator.
If you would like to borrow a calculator, pick one up now.

45. December 11, 2014 District Benchmark Assessment
You will not receive extra time after class (except for IEP or 504), so use your time wisely.
Write your name and the date on the front page.
You will receive a bubble sheet after you receive your test.
#1-6 are multiple select – there could be more than one correct answer. You must choose all of the correct options. Record your answers on the bubble sheet.
Write your answers to #7-12 on the test.
When finished, put your bubble sheet inside your test and turn it in to Mr. Szwast

47. Warm-Up: December 12, 2014
What inputs do not work in the function ?

48. Test Make-Ups
If you did not take the Chapter 4 Test or the District Benchmark, you can take either (or both) today after school, in this room.

49. Chapters 1-3 Test Retakes
You will have one opportunity to retake each test in January.
Each test will be offered on one specific day at a specific time. This is the only time you may retake it.
Before retaking, you must do all 3 of the following:
Get your previous test signed by a parent/guardian
Complete all missing/incomplete assignments from the chapter
Complete test corrections following the assigned format.
Eac

50. Chapters 1-3 Test Retakes
Chapter 1: Wednesday, January 7, 2:45-3:45
Chapter 2: Wednesday, January 14, 2:45-3:45
Chapter 3: Wednesday, January 21, 2:45-3:45
If you show up late, you may still retake it, but you must turn in your test by 3:45.
Signed test, test corrections, and missing homework assignments are due in class on Tuesday, the day before each test.

51. Homework Questions?

52. Function Inputs and Outputs
Section 5.05
Advanced Integrated Math I

53. Essential Question
How do we find the domain of a function?

54. Definitions The set of inputs is called the domain of the function.
The set of outputs that a function produces is called the range of the function.

55. A Juicer
What is the domain?
What is the range?

56. Library Catalog System
What is the domain?
What is the range?

57. You-Try (with partner)
Identify the domain and range for each:
The salary of a worker is a function of his or her skill level.
The price of an advertisement during a television show is a function of the number of viewers.
The magnitude of a sonic boom is a function of an airplane’s weight and fuselage length.

58. Example
What is the domain of the following function?

59. You-Try (with partner)
Find the domain of each of the following functions.

60. Assignment Read pages 383-384 Page 386 #7-10, 12
Bring your textbook on Monday
If you have a smartphone, you may instead take pictures of pages and use that in class on Monday.

61. Page 386

63. Warm-Up: December 15, 2014
Write the equation of the line, in slope-intercept form, that passes through (-1, 2) and (2, 6).

64. Homework Questions?

65. Section 5.06 Advanced Integrated Math I
Graphing Functions
Section 5.06
Advanced Integrated Math I

66. Essential Question
What can we learn about relations from their graphs?

67. Directions Read the “Minds in Action” on pages 387-388.
Play three rounds of the Guess My Rule game against your partner using Tony’s graphing method.
Each person is the Rule Maker 3 times and each person is the Rule Guesser 3 times.
With your partner, answer “For Discussion” #2, 3 on page 388
Read the “Minds in Action” on page 389
With your partner, answer “For Discussion” #4 on page 390

68. Answers
The y-coordinate of the intersection point gives the value of f(-2), which is 8. f(0)=3
0.5 and 5.5
Graphs 2 and 4 are functions; graph 1 is not a function.
Explain vertical line test
Examples of functions and non-functions:

69. Assignments
Page 392 #8, 9, 12, 13, 16-18
Page 396 #1-7