1. Warm up
It’s Hat Day at the Braves game and every child 10 years old and younger gets a team Braves hat at Gate 7. The policies at the game are very strict.
Every child entering Gate 7 must get a hat.
Every child entering Gate 7 must wear the hat.
Only children age 10 or younger can enter Gate 7.
No child shall wear a different hat than the one given to them at the gate.
1. What might be implied if all the rules were followed but there were still children 10 years old and younger in the ballpark without hats?
Those kids may NOT have entered through Gate 7.

2. Functions vs Relations

3. Relation
Any set of input that has an output

4. Function A relation where EACH input has exactly ONE output
Each element from the domain is paired with one and only one element from the range

5. Domain
x – coordinates
Independent variable
Input

6. Range
y – coordinates
Dependent variable
Output

7. Revisit the warm up:
It’s Hat Day at the Braves game and every child 10 years old and younger gets a team Braves hat at Gate 7. The policies at the game are very strict.
Every child entering Gate 7 must get a hat.
Every child entering Gate 7 must wear the hat.
Only children age 10 or younger can enter Gate 7.
No child shall wear a different hat than the one given to them at the gate.
What is the gate’s input?
What is the gate’s output?
Going in: Children 10 & younger without hats
Coming out of Gate 7: Children 10 & younger WITH hats

8. How do I know it’s a function?
Look at the input and output table – Each input must have exactly one output.
Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

9. function Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)}
Function or relation?
Example 1:
{(3, 2), (4, 3), (5, 4), (6, 5)}
function

10. Function or relation?
Example 2:
Function

11. Function or relation?
Example 3:
relation

12. function Function or relation? Example 4:
( x, y) = (student’s name, shirt color)
function

13. Function or relation?
Example 5: Red Graph
relation

14. function Function or relation? Jacob Angela Nick Honda Greg Toyota
Example 6
Jacob
Angela
Nick
Greg
Tayla
Trevor
Honda
Toyota
Ford
function

15. function A person’s cell phone number versus their name.
Function or relation?
Example 7
A person’s cell phone number versus their name.
function

16. Function Notation

17. Function form of an equation
A way to name a function
f(x) is a fancy way of writing “y” in an equation.
Pronounced “f of x”

18. Evaluating Functions

19. Tell me what you get when x is -2.
8. Evaluating a function
Tell me what you get when x is -2.
f(x) = 2x – 3 when x = -2
f(-2) = 2(-2) – 3
f(-2) = - 4 – 3
f(-2) = - 7

20. Tell me what you get when x is 3.
9. Evaluating a function
Tell me what you get when x is 3.
f(x) = 32(2)x when x = 3
f(3) = 32(2)3
f(3) = 256

21. Tell me what you get when x is -3.
10. Evaluating a function
Tell me what you get when x is -3.
f(x) = x2 – 2x + 3 find f(-3)
f(-3) = (-3)2 – 2(-3) + 3
f(-3) =
f(-3) = 18

22. Tell me what you get when x is 3.
11. Evaluating a function
Tell me what you get when x is 3.
f(x) = 3x + 1 find f(3)
f(3) =
f(3) = 28

23. Only list repeats once Put in order from least to greatest
Domain and Range
Only list repeats once
Put in order from least to greatest

24. 12. What are the Domain and Range?
{1, 2, 3, 4, 5, 6}
{1, 3, 6, 10, 15, 21}

25. 13. What are the Domain and Range?
{0, 1, 2, 3, 4}
{1, 2, 4, 8, 16}

26. 14. What are the Domain and Range?
All Reals
All Reals

27. 15. What are the Domain and Range?
x ≥ -1
All Reals