1. CH 1.2
FUNctions

2. I will be calling on random people to share your group’s ideas
Warm Up: Talk with your partners about the following. Write your group’s answers down
1) What does the word “relation” mean to you. Give examples.
2) What is a relation in math?
A rule of correspondence that connects elements from one set (usually denoted by ‘x’) with elements from a different set (usually denoted by ‘y’)
*AKA a connection(relationship) between two or more items (x and y)
3) What is a function?
A function is a rule of correspondence that assigns each element in one set EXACTLY one element in the second set.
*AKA a relation with CERTANTY
4) How are relations and a functions related?
A function IS a relation.
A RELATIONSHIP is an connection between things (usually two or more concepts, objects, or people
A RELATIONSHIP is an connection between things (usually two or more concepts, objects, or people)
You have RELATIONSHIPS with family members, friends, boyfriends/girlfriends, co-workers, teachers, other classmates, etc.
Make set notation
I will be calling on random people to share your group’s ideas

3. Instructions
were going to talk explore more about functions and when they exist. There are 4 signs around the room, one in each corner. After I read the first scenario, you will go to the corner that is true for you.

4. If you walked to school today, stand under A.
If you rode your bike to school today, stand under B.
If you drove or rode in a vehicle today, stand under C.
If you got to school any other way, stand under D.

5. If it took you fewer than 10 minutes to get to school today, stand under B.
If it took you 10 or more minutes to get to school today, stand under D.

6. If you’re an only child, stand under A.
If you have only one other sibling, stand under B.
If you have only two other siblings, stand under C.
If you have three or more other siblings, stand under D.

7. If you’re wearing blue, stand under A.
If you’re wearing red, stand under B.
If you’re wearing black, stand under C.
If you’re wearing white, stand under D.

8. If you were born in the first half of any month, stand under A.
If you were born in the second half of any month, stand under B.
If you were born in the first half of the year, stand under C.
If you were born in the second half of the year, stand under D.

9. Which of the examples were functions (relationships with certainty)?
Then have them discuss with partner for two minutes.
Call on volunteers for guesses.

10. Functions vs. Not Function
Transportation
If you walked to school today, stand under A. If you rode your bike to school today, stand under B. If you drove or rode in a vehicle today, stand under C. If you got to school any other way, stand under D.
Duration
If it took you fewer than 10 minutes to get to school today, stand under B. If it took you 10 or more minutes to get to school today, stand under D.
Siblings
If you’re an only child, stand under A. If you have only one other sibling, stand under B. If you have only two other siblings, stand under C. If you have three or more other siblings, stand under D.
Clothes
If you’re wearing blue, stand under A. If you’re wearing red, stand under B. If you’re wearing black, stand under C. If you’re wearing white, stand under D.
Birthday
If you were born in the first half of any month, stand under A.
If you were born in the second half of any month, stand under B. If you were born in the first half of the year, stand under C. If you were born in the second half of the year, stand under D.
Now lets add formal language to the concepts we’ve just felt.
“Mathematicians call the first three relationships ‘functions.’ Why? DRAW STUDENT EXS ON WHITEBOARD.
Each element of domain must be matched with an element of range.
Some elements of range may not be matched, or matched with two elements of domain
Why do you think these relationships aren’t functions?”
An element of the domain cannot be matched with two elements of the range.

11. Each element of domain must be matched with an element of range.
Some elements of range may not be matched
Two elements of the domain may be matched with the same range.
One element of the domain cannot be matched with two elements of the range.
USE WHITEBOARD STUDENT EXAMPLES
So all of you are the domain and you all need a place to go
Its ok if some of you did not bike to school, the options don’t need to be all used
More than one of you may have used the same mode of transportation
But you didn’t get to school by two of the options

12. Some Common ways to represent functions are….
Verbally
Numerically
Graphically
Algebraically

13. “test” to visually determine if a graph is a function?
Is there a quick way, or
“test” to visually determine
if a graph is a function?
Why does it work?
Yes, yes, yes, no

14. Write points on the board
If you are looking at a graph, you can easily see if an X has more than 1 Y.
Can you be in two places at once? Your timeline of your life and where you are at any given point is a function

15. Some of my favorite equations! Which ones are not a functions

16. Determine whether each relation is a function cont.
y =1- x² –x + y² = 1

17. HW Questions
Switch your hw with one other partner. Please put “CB: your name” on the top of the page.
Get out the yellow “hw guidelines” half sheet of paper we looked at last class. Check that they have followed the directions. Make notes for improvements.
Discuss any questions/incorrect answers and see if someone at your table knows how to solve.
When you are finished, make a pile in the center of the table so I know you are ready to move on.

18. Let’s talk about the basic parent functions you have seen in Alg 2… 4 Color Exploration
In groups, you will be given a set of cards
The pink cards are the Graphs
The yellow cards are the name of the function
The green cards are the equation of the function
The purple cards are the domain/ranges
Match each pink, yellow, green, and purple card together appropriately. Most functions you should have seen before in Algebra 2. Use process of elimination if you get stuck.
Once you have made all matches, discuss with your group any terms/symbols/functions that you may not know. I will be calling on random groups.

19. Ch 1.1 Notes: An Overview of Functions
Vertex
zero
INCLUDE CONSTANT FUNCTION

26. Now that we have reviewed our basic parent functions, lets talk about a few more specific ways to describe them!

27. What is function notation?
f(x)
y-value f
f(x)
Or “y” x y

28. EX 1: Finding Domain and Range

31. ASK SIRI

32. Ex: What is the implied domain of

33. HW
Pg 24 #1-6all, 9, 15-27odd, 54-57all, 86a/b onliny