1. Functions Review Today’s Agenda Do Now Questions Review
LT:
I will study to be ready for my assessment
Today’s Agenda
Do Now
Questions
Review
Success Criteria
II can prepare for my assessment

2. Clear your desk including back packs Put away your phones
Functions Test
LT:
I will add, subtract and multiply functions. Describe the domain and range and describe key features of a function.
Test:
Clear your desk including back packs
Put away your phones
Make sure you have a pencil and eraser
When finished put your test in the box
Two sheets of hand written notes are permitted
Please -no talking during the Test
Remain quiet until everyone is finished
Today’s Agenda
Test
Success Criteria
II can add, subtract and multiply functions. Describe the domain and range and describe key features of a function.

3. Review: What is a function?
A relationship where every domain (x value has exactly one unique range (y value).
Sometimes we talk about a FUNCTION MACHINE, where a rule is applied to each input of x

4. Domain and Range x x Solve for x if i(x)=12 Do Now Lesson
LT:
I will be able to evaluate functions and identify key concepts from graph, table, or algebraically. x
f(x) x
f(x)
Solve for x if i(x)=12
Today’s Agenda
Do Now
Lesson
Class activity
HW#8
Success Criteria
I can evaluate functions and identify key concepts from the graph, table , or algebraically

5. Pull out HW# 7

6. Recreate the graph on your poster
Describe the x-axis and y-axis
Are there any x and y intercepts and how do you know ( what if x=0 and what if y=0)-describe it
Describe the Domain in your own words
How do you know
Use set builder notation and interval notation to describe the domain
Describe the Range in your own words
Use set builder notation and interval notation to describe the Range
Be prepared to describe your poster to the class
Task Master
Artist
Presenter
Re-voicer

7. HW# 8
Work in pairs-Not Groups

8. Hand out Activity

9. Adding and Subtracting functions
LT:
I will learn that functions can be added and subtracted.
Today’s Agenda
Do Now
Activity
Lesson
HW#9
Success Criteria
I can add and subtract functions

10. Adding and Subtracting functions
LT:
I will learn that functions can be added and subtracted.
Today’s Agenda
Do Now
Lesson
HW#10
Success Criteria
I can add and subtract functions

11. Function Operations

12. Combine like terms & put in descending order
The sum f + g
This just says that to find the sum of two functions, add them together. You should simplify by finding like terms.
Combine like terms & put in descending order

13. Adding Linear Functions
f(x) + g(x)
If f(x)= 3x - 4 and g(x) = -2x + 6,
find f(x) + g(x).
(3x – 4) + (-2x + 6) OR
3x – 4
+ -2x +6
1x + 2
So, f(x) + g(x) = 1x + 2

14. Adding Linear Functions
If f(x) = 7x + 3 and g(x) = 6x – 4,
find f(x) + g(x).

15. The difference f - g Distribute negative
To find the difference between two functions, subtract the first from the second. CAUTION: Make sure you distribute the – to each term of the second function. You should simplify by combining like terms.
Distribute negative

16. Adding and Subtracting Functions
When we look at functions we also want to look at their domains (valid x values). In this case, the domain is all real numbers.

17. Subtracting Linear Functions
f(x) - g(x)
If f(x) = 4x -29 and g(x)= 2x – 18,
find f(x) – g(x).
(4x – 29) – (2x -18) change – to + the opposite.
(4x – 29) + (-2x +18) Or
4x – 29
+ -2x + 18
2x - 11
So, f(x) – g(x) = 2x – 11

18. Subtracting Linear Functions
If f(x) = -3x + 15 and g(x) = -4x -17, find f(x) – g(x).

19. HW#9

20. Adding and Subtracting functions
I will learn that functions can be added and subtracted.
LT:
I will be able to evaluate functions and identify key concepts from graph, table, or algebraically.
What is the domain
What is the range
At what intervals is the function increasing
At what intervals is the function decreasing
Where are the x intercepts
Where are the y intercepts
Today’s Agenda
Do Now
Review
Catch up day
Quiz tomorrow
Success Criteria
I can add and subtract functions
I can evaluate functions and identify key concepts form a graph, table, or algebraically

21. Adding and Subtracting functions And Domain and Range
I will learn that functions can be added and subtracted.
LT:
I will be able to evaluate functions and identify key concepts from graph, table, or algebraically.
Quiz:
Clear your desk including back packs
Put away your phones
Make sure you have a pencil and eraser
When finished, staple your quiz and put it in the box
HW#8, 9 & 10 are the only notes permitted
No talking during the quiz and remain quiet until everyone is finished
Today’s Agenda
Quiz
Work on unfinished assignments
Success Criteria
I can add and subtract functions
I can evaluate functions and identify key concepts form a graph, table, or algebraically

22. Multiplying Functions
I will multiply functions using different methods
Do Now
1. 33 27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4 16
4. n2r for n = 3 and r = 2 18
Today’s Agenda
Do Now
Hand Back Quiz
Lesson
HW#11
Success Criteria
I can multiply functions using different methods

23. Multiplying Polynomials

24. The Distributive Property
(x + 5)(2x + 6)
(x+5) 2x + (x+5)6
2x(x+5) +6(x+5)
2x² + 10x + 6x + 30
2x² + 16x +30
NOTE : Since there are THREE terms this is called a TRINOMIAL

25. Area Model
(4x+3)(2x+9) 4x 2x 9

26. Trinomials Multiplying MOST binomials results in THREE terms
You can learn to multiply binomials in your head by using a method called
F O I L

27. first terms last terms (x + 4) ( x + 2) inner terms outer terms
The FOIL Method
(x + 4)(x +2)
first terms last terms
(x + 4) ( x + 2)
inner terms
outer terms

28. terms terms terms terms
(x + 4) ( x + 2)
Now write the products
x² x x
first outer inner last
terms terms terms terms

29. multiply the first two terms multiply the two outer terms
To Multiply any two binomials and write the result as a TRINOMIAL follow these steps
multiply the first two terms
multiply the two outer terms
multiply the two inner terms
multiply the last two terms

30. Using FOIL k ² + 4k - 4k - 16 k ² - 16 (6c – 3) ( 6c + 3)
A Closer Look
(k – 4) (k + 4)
Using FOIL
k ² + 4k - 4k
k ² - 16
(6c – 3) ( 6c + 3)
36c² +18c – 18c – 9

31. Special Cases Difference of Squares Perfect Square Trinomials
There are several special cases of multiplying binomials
Difference of Squares
Perfect Square Trinomials

32. Difference of two squares
When you multiply the sum of two terms and the difference of two terms you get a BINOMIAL
(a + b) (a – b) = a² - b²
This binomial is the difference of two squares

33. Good idea to put in descending order but not required.
The product f • g
To find the product of two functions, put parenthesis around them and multiply each term from the first function to each term of the second function.
FOIL
Good idea to put in descending order but not required.

34. Multiplying Functions
In this case, the domain is all real numbers because there are no values that will make the function invalid.

35. Dividing Functions
In this case, the domain is all real numbers EXCEPT -1, because x=-1 would give a zero in the denominator.

36. Nothing more you could do here. (If you can reduce these you should).
The quotient f /g
To find the quotient of two functions, put the first one over the second.
Nothing more you could do here. (If you can reduce these you should).

37. Let’s Try Some
What is the domain?

38. Perform each operation
Pg. 401
#9-75 by 3s

39. Let’s Try Some
What is the domain?

40. Let’s Try Some
What is the domain?

41. Let’s Try Some
What is the domain?

42. Composite Function – When you combine two or more functions
The composition of function g with function is written as 1
1. Evaluate the inner function f(x) first.
2. Then use your answer as the input of the outer function g(x). 2

43. Example – Composition of Functions
Method 1:
Method 2:

44. Let’s try some

45. Solution

46. Solving with a Graphing Calculator
Start with the y= list.
Input x3 for Y1 and x2+7 for Y2
Now go back to the home screen.
Press VARS, YVARS and select 1. You will get the list of functions.
Using VARS and YVARS enter the function as Y2(Y1(2).
You should get 71 as a solution.

47. Real Life Application
You are shopping in a store that is offering 20% off everything. You also have a coupon for $5 off any item.
Write functions for the two situations.
Let x = original price.
20% discount: f(x) = x – 0.20x = 0.8x
Cost with the coupon: g(x) = x - 5

48. 2. Make a composition of functions:
You are shopping in a store that is offering 20% off everything. You also have a coupon for $5 off any item.
2. Make a composition of functions:
This represents if they clerk does the discount first, then takes $5 off the discounted price.

49. 3. Now try applying the $5 coupon first, then taking 20% off:
You are shopping in a store that is offering 20% off everything. You also have a coupon for $5 off any item.
3. Now try applying the $5 coupon first, then taking 20% off:
How much more will it be if the clerk applies the coupon BEFORE the discount?

50. 4. Subtract the two functions:
You are shopping in a store that is offering 20% off everything. You also have a coupon for $5 off any item.
4. Subtract the two functions:
Any item will be $1 more if the coupon is applied first. You will save $1 if you take the discount, then use the coupon.