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. Coordinate Algebra
UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems?
Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5
Today’s Question:
What is a function?
Standard: MCC9-12.F.IF.1 and 2

3. Coordinate Algebra - IN
Standards:
MCC9-12.F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

4. Functions vs Relations

5. Relation
Any set of input that has an output

6. Function
A relation where EACH input has exactly ONE output

7. Domain
Input
x – coordinates
Independent variable

8. Range
Output
y – coordinates
Dependent variable

9. 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

10. 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

11. Function or relation?
Example 2:
relation

12. Function or relation?
Example 3:
relation

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

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

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

16. 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

17. The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home.
What do the horizontal lines on the graph represent?
Where in the graph shows her taking care of the 2 errands?
Compare how she traveled at the beginning to how she traveled at the very end.
Create Maria’s story so that it matches the graph.

18. MCC9-12.F.IF.4 (p. 51)
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.

19. Characteristics of Functions

20. Intercepts
x-intercept – the point at which the line intersects the x-axis at (x, 0)
y-intercept – the point at which the line intersects the y-axis at (0, y)

21. Find the x and y intercepts, then graph.
-3x + 2y = 12

22. End Behavior
Sweep from left to right and notice what happens to the y-values
Increasing goes up (L to R)
Decreasing falls down (L to R)
Constant is a horizontal graph

23. Continuous vs Discrete
Continuous has NO breaks
Discrete has gaps or breaks

24. Extrema Maximum Point – greatest value of the function
Minimum Point – least value of the function

25. Domain & Range Domain – all x-values of a function
Range – all y-values of a function

26. Notation for Domain and Range
Interval – represents an interval as a pair of numbers. The numbers are the endpoints of the interval.

27. [Brackets]
brackets are used to show that the endpoints are included

28. (Parentheses)
Used to show that the endpoints are excluded

29. {Set with no interval}
List the numbers in order without repeat