1. Unit 2: Data and Function Fitting
With a Transformations of Parent Functions

2. Lesson 1: Linear vs. Non-Linear Data Objective: SWBAT identify linear and nonlinear data trends Keep on your desk: HW from Monday

3. Lesson 1 Day 1 – 09/01/15 Linear vs
Lesson 1 Day 1 – 09/01/15 Linear vs. Non-Linear Data Objective: SWBAT identify linear and nonlinear data trends Keep on your desk: HW from Monday

4. Stroop Test Data Collection
Take 5-10 minutes to finish data collection process
Graph the List Length vs. Time on an x-y coordinate plane with a triangle and circle (according to your page)
We will begin Part 2 of your test (Data Analysis) in 12 minutes

5. Stroop Test – Performance Assessment
Your predictions (top two bubbles) do not have a single correct answer. Just predict!
For the next two parts, look at the best-fit line that YOU drew on your graph for each set of data (triangles and circles). Choose (estimate) coordinate pairs that fall EXACTLY on the line. They don’t have to be from your data! They can be a crosshair where the line goes through.
Self-explanatory from there

6. Correlation of a Linear Data Set
Examples of correlations and their correlation coefficients (r values) for LINEAR MODELS

7. Notes on Correlation and Trend Lines
“Regression Line” = “Trend Line” = “Best-Fit Line”
Correlation – the strength of the relationship of a data set
The Correlation Coefficient is a number that tells you the strength of that relationship.
𝟎≤ 𝒓 ≤𝟏, but r can be negative. So, actually, −1≤𝑟≤1.
The coefficient of determination, denoted R2 or r2 and pronounced ”R squared”, is a number that indicates how well the data fits a model equation. It signifies the “spread” of the data
This number is simply the square of the r value, and it will range from 0 to 1.
0 means the data is very spread out from the model
1 means the data is very tightly packed to the model

8. When to use r vs. 𝑟 2 Correlation coefficient – r
When you are determining the type of correlation or relationship that the data have (positive, negative, none)
Not every kind of regression model has an “r” value. Some only have 𝒓 𝟐 . This is because not every model can have a “positive” and a “negative” correlation.
Coefficient of determination - 𝑟 2
When you are determining if a model is “reasonable” to use for a particular data set
When you are comparing different function models (linear vs. quadratic vs. logarithmic vs. exponential, etc.) – This is using the “STAT”  “CALC” menu with all of the “Reg”s

9. Exit Ticket – In pairs of 2
Do “Lesson Check” on page 96 #1-3 – check in with teacher’s textbook at front of room after each one

10. HOMEWORK (Due Thursday):
Go back and adjust your answers to #7-14 ALL on pages given what we talked about in class
In addition to those, DO page 97 #18

11. Lesson 1 Day 2 – 09/03/15 Linear vs
Lesson 1 Day 2 – 09/03/15 Linear vs. Non-Linear Data Objective: SWBAT identify linear and nonlinear data trends Keep on your desk: HW from Tuesday

12. HW Questions?
In your pods, decide on ONE question that you have as a group. In doing so, help answer each other’s questions.
Have one person write your question on the board in the spaces accordingly
After finished with questions, turn HW into the tray.

13. Practice Some Linear Regression!
Using the steps on your calculator
1. Enter the data into your calculator
“STAT”  “1.Edit”  ENTER  Enter x into L1, y in L2
If L1 or L2 are not there… Go to “STAT”  “5:SetupEditor”  ENTER twice. Go back and see them.
2. Find the linear regression equation
“STAT”  “CALC” Menu  “4:LinReg (ax+b)”  ENTER twice
3. Graph the data if you would like!
“Y=“  Go up to “PLOT 1” and make sure it is highlighted (if not, hit ENTER over it)  “ZOOM” “9”
4. Graph the regression equation if you would like!
“Y=“  Input the equation you found in step 2 above using the a and b value along with “X,T,𝜃,n” button for X

14. HOMEWORK:
1) Complete Linear Regression worksheets – ALL problems – you’ll need your graphing calculators! – Due Tuesday
2) Make corrections on your pink tests for EVERY problem where you missed points (no checkmark is drawn). Use notes, books, and other resources! FOR EACH PROBLEM:
1. Number of problem
2. “What I did incorrectly was…”
3. Correct the problem and circle your answer
- Due Thursday (ask Q’s after school Tues)

15. Lesson 1 Day 3 – 09/08/15 Linear vs
Lesson 1 Day 3 – 09/08/15 Linear vs. Non-Linear Data Objective: SWBAT identify linear and nonlinear data trends Turn in to the tray: HW from the weekend (worksheets)

16. HOMEWORK (ALL Due Thursday)
1) Make corrections on your pink tests for EVERY problem where you missed points (no checkmark is drawn). Use notes, books, and other resources! FOR EACH PROBLEM:
1. Number of problem
2. “What I did incorrectly was…”
3. Correct the problem and circle your answer
2) Finish Group Data Presentation Details
3) READ and take notes on pages 41-45,

17. Data Analysis (Test Part 2) Return
Read through my comments on your Test Part 2’s silently.
General questions/comments? Individual questions after class please
Details matter!
Test grades – How do I improve? Do all of the following to gain up to the next highest letter grade (FD, DC, CB, BA)
Do your test corrections
After/before school on Thursday or Friday, come in for a re-test problem based on what you missed (must have corrections done already)
No exceptions – If this matters to you, then you must be there on one of those times for as long as I require!

18. Group Data Analysis
In groups of 3 or 4, you will be presented with some data.
You must graph the data on a giant graph paper and find the linear regression equation (y=mx+b) along with its correlation coefficient and coefficient of determination
You must also display two other regressions (found in the “STAT”  “CALC” menu) that have a higher coefficient of determination ( 𝒓 𝟐 ) than the linear regression
YOU WILL BE GRADED ON HOW WELL YOU DO YOUR JOB IN YOUR GROUP AND YOUR GROUP’S ANALYSIS
JOBS: (1) Pattern Analyst (2) Grapher/Plotter
(3) Presenter (4) if necessary – director/extra analyst

19. Group Data Analysis JOBS: (1) Grapher/Plotter (2) Pattern Analyst
(3) Presenter (4) if necessary - extra analyst or presenter
What you will turn in/be graded on:
Your giant graph of data along with three (diff. color) regression models through the data
Separate sheet of paper with all of the types of regressions you TRIED (even if you didn’t use it) with the equation AND 𝑟 2 value, along with r value if it is given.
- Also on sheet: Extrapolation with input value of 200 and extrapolation with output value of 5000.
Short (2-3 min) presentation about the different types of regression used, which one is best, which is worst, what the coefficient of determination says, and what your extrapolated input/output values are.
- Your group all needs to know what you are doing! Be time-efficient!

20. Lesson 2 Day 1 – 09/10/15 Absolute Value Function Objective: SWBAT Solve and Graph the Absolute Value Function Turn in to the tray: TEST Corrections!

21. HOMEWORK (ALL Due Friday)
Textbook Page 46 #11-29 Odds
Practice Quiz/Exploration
QUIZ tomorrow on Regression (Calculator steps and data analysis)
HONORS ONLY: Also page 46 #43-55 Odds

22. Data Analysis Presentations!
Present as if you are a department presenting to the CEO (Mr. Speer)
Speakly loudly and clearly
Don’t use “Um” or “like”
Explain the whole process, from start to finish
2-3 minutes long

23. Which type of Regression should we use?
It is helpful to know the general shape of some of the functions that are used in regression analysis.
Some common parent functions that are used to model data are:
Linear
Quadratic
Cubic
Absolute Value
Square Root
Exponential
Logarithmic
Rational
Sine
Cosine
Tangent
Let’s take a look at these (on yellow “Parent Functions Chart” sheet)

24. Example Absolute Value Problems
Problem 1 (page 42)
𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 2𝑥−1 =5 ?𝐺𝑟𝑎𝑝ℎ 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛.
SOLUTION:
𝟐𝒙−𝟏 =𝟓
Since |5|=5 and |-5|=5, then |2x-1| = positive or negative 5
𝑻𝒉𝒆𝒏 𝑥−1=5 𝑂𝑅 2𝑥−1=−5
+𝟏 +𝟏 𝟏 𝟏
2𝑥=6 𝑂𝑅 2𝑥=−4
÷𝟐 ÷𝟐 ÷𝟐 ÷𝟐
𝐱=𝟑 𝐎𝐑 𝐱=−𝟐
To graph, plot points on the number line at 3 and at -2.

25. Example Absolute Value Problems
Problem 4 (page 43) 𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 2𝑥−1 <5 ?𝐺𝑟𝑎𝑝ℎ 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛. SOLUTION: 𝟐𝒙−𝟏 <𝟓 Since |5|=5 and |-5|=5, then |2x-1| < positive 5 or > negative 5 𝑻𝒉𝒆𝒏 2𝑥−1<5 𝑂𝑅 2𝑥−1>−5 +𝟏 +𝟏 +𝟏 +𝟏 2𝑥<6 𝑂𝑅 2𝑥>−4 ÷𝟐 ÷𝟐 ÷𝟐 ÷𝟐 𝐱<𝟑 𝐎𝐑 𝐱>−𝟐 In one sentence, you could say that −𝟐<𝒙<𝟑, 𝒐𝒓 𝒙∈(−𝟐,𝟑) Graph: Plot a segment on the number line connecting -2 and 3, with OPEN dots at the endpoints, since -2 and 3 are NOT included as solutions. See page 43 of text.

26. Lesson 2 Day 2 – 09/11/15 Absolute Value Function Objective: SWBAT Solve and Graph the Absolute Value Function Keep to turn in on Monday: HW from textbook – QUIZ TODAY!

27. HOMEWORK (ALL Due Monday)
From Yesterday:
Textbook Page 46 #11-29 Odds
HONORS ONLY: Also page 46 #43-55 Odds
Also due Monday (NEW):
Regular: Page #31-35 odds, odds, #81
Honors: Page #31-35 odds, #57-65 Odd, #81
ALL CLASSES: Read page and try page 111 #9-15 Odds

28. Which is most difficult?
Out of the following three problems, take ONE minute to read them and determine which is most difficult. You may solve them only AFTER you have examined each of them.
Problem 1: Solve 3𝑥+4 =−3
Problem 2: Solve 3 5𝑡−1 +9≤23 and graph.
Problem 3: Solve 𝑥−4 +10≤11 and graph.

29. “Levels” Stations
Go to your station and complete the problems there in your group (or smaller pairs/triads)
Bring your notes! Reference the book! Sitting idly by while time ticks away is NOT what you should be doing.

30. You may leave when the bell rings.
Exit Ticket
At your station, there is an exit ticket. Take one, complete it, and turn it in to your class tray.
You may leave when the bell rings.

31. Lesson 2 Day 3 – 09/14/15 Absolute Value Function Objective: SWBAT Solve and Graph the Absolute Value Function Keep at your desk for review: HW from textbook pages

32. HOMEWORK (ALL Due Tuesday)
Using Problem 1 on page 108 as a guide, Do page 111 #8-16 Evens

33. HW Questions? Regular Algebra 2
What questions do you have from
Regular Algebra 2
Textbook Page 46 #11-29 Odds #31-35 odds, odds, #81,
Page 111 #9-15 Odds
Algebra 2 Honors
Textbook Page 46 #11-29 Odds #31-35 odds, odds, #81,

34. Checking for Extraneous Solutions
When working with any kind of equation, the final step should always be: “Does my answer make sense in the original problem?”
Extraneous solution: A “solution” that actually does not work as a solution to the original problem.
Example: Solve 5𝑥−2 =7𝑥+14
Solution:
𝟓𝒙−𝟐= 𝟕𝒙+𝟏𝟒 𝑶𝑹 𝟓𝒙−𝟐=−(𝟕𝒙+𝟏𝟒)
𝒙=−𝟖 𝑶𝑹 𝒙=−𝟏
However, when plugging x=-8 into the original equation,
𝟓 −𝟖 −𝟐 =𝟕 −𝟖 +𝟏𝟒, 𝒂𝒏𝒅 𝟒𝟐=−𝟒𝟐 →𝑾𝑹𝑶𝑵𝑮

35. Checking for Extraneous Solutions
Additional Examples – page 46 #20,22,24

36. Lesson 3 Day 1 – 09/15/15 Parent Function Translations Objective: SWBAT Generalize the translations of absolute value functions to all parent function graphs Keep at your desk for review: HW from textbook pages

37. Quick Quiz time!
Clear your desks, but keep your calculator and pencil out.
Extra Credit (write your answer on the back of the quiz)
What is the motto of the University of Notre Dame?
Hint: It had something to do with the Virgin Mary…

38. After the quiz…. WARMUP!
Try the following problem…
1. Graph the function 𝑦=|𝑥| and 𝑦= 𝑥 +3 by hand on the same graph with a table of values.
2. What is the difference between the two graphs in #1?
3. Try graphing 𝑦= 𝑥 and 𝑦= 𝑥+3 in the same way. Does the same thing happen as in #1?

39. Absolute Value Parent Function 𝑦=|𝑥|

40. Transformations of the Absolute Value Function
What if it wasn’t just 𝑦= 𝑥 ? What if we had 𝑦= 𝑥 −2 or 𝑦= 𝑥−4 ?
Transformations:
𝑦= 𝑥 +𝑘 for any value k – Translates the parent function up/down by k units.
𝑦= 𝑥−ℎ for any value h – Translates the parent function right/left by h units.
𝑦=−|𝑥|  flips the graph across the x-axis (upside down V)
𝑦=𝑎|𝑥| for any value a – stretches the absolute value parent function vertically (multiply y-values by a)

41. Exit Problem On whiteboards
On the blank side, describe the transformation happening to the parent function.
Make a table of 5 values and graph the transformed function on the graph side.
Function: 𝑦= 𝑥+4 −2

42. HOMEWORK (ALL Due Thursday)
Worksheet on Graphing Absolute Value Transformations – ALL
Draw the parent function,
Describe what the transformed graph looks like
Create a table of values and graph the transformed in a different color.

43. Lesson 3 Day 2 – 09/17/15 Parent Function Translations Objective: SWBAT Generalize the translations of absolute value functions to all parent function graphs To Turn in LATER: Worksheet on absolute value graphs and book problems that were due on tuesday

44. Warmup
- Finish Page 3 of worksheet from Tuesday – Matching graphs #1-6 to equations a-f. - Write the letter of the equation next to each graph. - Try not using your calculator, but use it if you MUST.

45. Warmup (Honors) Bonus: Try 𝑦=− 𝑥−3 −4 On whiteboards
Function: 𝑦= 𝑥−1 +3
On the blank side, describe the transformation happening to the parent function.
Make a table of 5 values and graph the transformed function on the graph side.
Bonus: Try 𝑦=− 𝑥−3 −4

46. Transformations of the Absolute Value Function
What if it wasn’t just 𝑦= 𝑥 ? What if we had 𝑦= 𝑥 −2 or 𝑦= 𝑥−4 ?
Transformations:
𝑦= 𝑥 +𝑘 for any value k – Translates the parent function up/down by k units.
𝑦= 𝑥−ℎ for any value h – Translates the parent function right/left by h units.
𝑦=−|𝑥|  flips the graph across the x-axis (upside down V)
𝑦=𝑎|𝑥| for any value a – stretches the absolute value parent function vertically (multiply y-values by a)

47. Transformations of Parent Functions
Using your yellow parent functions sheet, do this on whiteboards:
On the blank side:
a. Identify the parent function (name)
b. Describe the transformation happening to the parent function.
2. Make a table of 3 accurate values and graph the transformed function on the graph side.

48. 𝑦=− 𝑥 𝑦= (𝑥+1) 2 𝑦= 𝑥 +2 𝑦= 𝑥−4 3 𝑦= 1 𝑥−2 Ready…? Go!
𝑦= 𝑥 +2
𝑦= 𝑥−4 3
𝑦= 1 𝑥−2
- Parent: Absolute Value
- Reflected across the x-axis
- Parent: Quadratic
- Shifted left by 1 unit
- Parent: Square Root
- Shifted up by 2 units
- Parent: Cubic
- Shifted right by 4 units
- Parent: Rational
- Shifted right by 2 units

49. HOMEWORK (ALL Due Monday)
HW 2.4 Worksheet on Graphing Transformed Parent Functions- ALL problems

50. Lesson 3 Day 3 – 09/21/15 Parent Function Translations Objective: SWBAT Generalize the translations of absolute value functions to all parent function graphs To be checked: HW 2.4 Worksheet

51. ACT PREP WARMUP Answer: F (3,-7)
In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?
F. (3,–7)
G. (4,–8)
H. (5,–1)
J. (8,–3)
K. (9,–3)
Answer: F (3,-7)

52. Homework Questions?
Please ask now!

53. Whiteboard Quiz Use the following functions: 1. 𝑦= 𝑥+1 2 2. 𝑦=− 𝑥−5
1. 𝑦= 𝑥+1 2
2. 𝑦=− 𝑥−5
3. 𝑦= 𝑋+2
4. 𝑦= 𝑥+3 2
5. 𝑦= 𝑥+2 −3
6. 𝑦=− 𝑥−1 2
7. 𝑦=− 𝑥 +4
8. 𝑦=− 𝑥−1 2
9. 𝑦=− 𝑥−2 +4
10. 𝑦=− 𝑥+1 −3

54. Finish Stretch and Reflection Exploration worksheet packet
Homework due Tuesday
Finish Stretch and Reflection Exploration worksheet packet
Quiz tomorrow on parent function graphs and shifts/reflections

55. Lesson 4 Day 1 – 09/22/15 Parent Function Dilations Objective: SWBAT Generalize the Dilations of absolute value functions to all parent function graphs To check solutions: Hw worksheet from Monday night

56. HW Solutions Check
Check that you have the exact answers to the homework on the document camera!
These are to be used as study tools for the test on Friday!

57. Vertical Dilations of Parent Functions
What happens when you graph 𝑦=𝑎∙𝑓 𝑥 , where a is some number that is being multiplied by a parent function f(x)?
We call these dilations.
Observations/Summary of dilations:
Q1: What do you notice about the graphs of a∙f(x) when a > 1, in each part b on the front side (compared to the graphs in part a)?
A1: When you graph a∙f(x) when a > 1, the graph is stretched vertically by a factor of a.
Q2: What do you notice about the graphs of a∙f(x) when a < 1, in each part c on the front side (compared to the graphs in part a)?
A2: When you graph a∙f(x) when a < 1, the graph is compressed vertically by a factor of a.
(To do all of this, keep x values the same, and multiply y-values by ‘a’)

58. On your own paper... For each of the following,
(a) identify the parent function
(b) Describe the transformations applied to the parent
(c) Graph the function on a separate sheet of graph paper
1. 𝒚=𝟐 𝒙−𝟑 𝟑
2. 𝒇 𝒙 =𝟑 𝒙 −𝟐
3. 𝐠 𝒙 = 𝟏 𝟐 𝒙+𝟏 𝟐
4. 𝒚=−𝟒|𝒙|

59. Clear your desks except for a pencil.
Quick Quiz time!
Clear your desks except for a pencil.

60. Complete HW 2.5 worksheet on parent graphs and transformations
Homework due Thursday
Complete HW 2.5 worksheet on parent graphs and transformations
Test on Friday!
Regression, Correlation, etc.
Absolute Value Equations/Ineqs
Parent Function Transformations

61. Lesson 4 Day 2 – 09/24/15 Parent Function Dilations Objective: SWBAT Generalize the Dilations of absolute value functions to all parent function graphs To display on the board: HW 2.5 Worksheet QUIZ After!

62. Homework Review Please post either: Parts (a) and (b) to a problem OR
The graph of a problem
Everyone should have one problem to show. If you have one that you did not complete or did not understand, now is your chance to ask questions and build understanding! Ask a classmate first, then ask Mr. Speer!

63. Remove everything from your desk EXCEPT: 1. Pencil
Quiz Time!
Remove everything from your desk EXCEPT:
1. Pencil
2. Homework (2.5 Worksheet)

64. Test on Monday
Topics: 1. Regression Analysis  2. Absolute Value Equations and Inequalities  3. Graphing the Absolute Value and other Parent Graphs  4. Parent Functions and Transformations 

65. Homework
Complete worksheet #2.6 FRONT Side and try at least one problem from the “Challenge” side.
Continue studying for the test; come with at least one question about a topic!

66. Lesson 4 Day 3 – 09/25/15 Parent Function Dilations Objective: SWBAT Generalize the Dilations of absolute value functions to all parent function graphs To check in class: HW 2.6 Worksheet

67. Warmup – Transform a point!
Transform the following points using all of the following transformations together:
Reflected across the x-axis
Compressed vertically by a factor of 1 3
Shifted to the left by 4
Shifted down by 6
(0,0)
(2,4)
(9,3)
(-4,-6)
(5,-7)
(-2, )

68. HW Questions? Transformations
When graphing a function, use the following tips:
Any number on the inside of the function applies to the x-values.
Any number on the outside of the function applies to the y-values.
Adding/Subtracting = shifting
Multiplying = stretching/shrinking
MEMORIZE the parent function graph coordinate pairs and transform them one at a time
Examples:
For square root, the coordinate pairs are (0,0) (1,1) (4,2) and (9,3)

69. Group Review Questions – “TEST REVIEW” Piece of paper
In your textbook, try at least 2 from each of the following sets of problems
page 125 #31-35, 37-38,
page 52 #27-34 All
page 126 #40-47,
page 127 #33-37,

70. Complete the Study Guide for the TEST on MONDAY
Homework
Complete the Study Guide for the TEST on MONDAY
Study for TEST MONDAY! Look through notes, handouts, and quizzes!

71. ACT PREP WARMUP A. 2 B. 4 C. 8 D. 12 E. 16 Answer: B. 4
The volume, V, of the right circular cone with radius r and height h, shown below, can be found using the formula
𝑉 = 1 3 𝜋 𝑟2ℎ. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?
A.   2
B.   4
C.   8
D. 12
E. 16
Answer: B. 4

72. TEST TIME SILENCE is required for the ENTIRE period.
Please leave your study guides (completed for HW) on the bottom tray underneath your chair.
NO TALKING
When you finish your calculator portion, please bring your test and calculator to me and receive the non-calculator portion.
When finished, please remain quietly in your seats and work on something else.
DO NOT TALK.
Pace yourself! You have 55 minutes.