1. Day 8
Relations
Represent relations
Interpret graphs of relations

2. Using a coordinate graph system http://www. coolmath
Coordinate system
Ordered pairs (x, y)
Quadrants I, II, III, IV
Y- coordinate
X- coordinate
X-axis
Y-axis

3. Representation of a Relation
Domain and Range
Ordered Pairs: (1,2), (-2, 4), (0, -3)
Table Graph Map x y

4. Representation of a Relation
Domain and Range
Ordered Pairs: (2,5), (-2, 3), (5, -2), (-1, -2)
Table Graph Map x y

5. What are three ways to represent a relation?
* Show {(4, -3), (3,2, (-4,1), (0, -3)} as a relation in three ways.

6. Independent and Dependent variables
Identify the independent and dependent variables:
The committee is selling tickets to the Fall Ball. The tickets that they sell, the greater the amount of money they can spend for decorations.
Independent: Dependent:
Generally, the average price of going to the movies has steadily increased over time.
The air pressure inside a tire increases with the temperature.
As the amount of rain decreases, so does the water level of the river.

7. Interpreting graphs

8. Determine whether a relation is a function Find function values
Functions
Determine whether a relation is a function
Find function values

9. What is a function?
A function is a relationship between input and out put. In a function there is exactly one output for each input.
A function is a relation in which each element of the domain is paired with exactly one element of the range
Domain Range -3 3 4 5 3 2 1

10. What is a function?
A function is a relationship between input and out put. In a function there is exactly one output for each input.
A function is a relation in which each element of the domain is paired with exactly one element of the range
Domain Range -2 3 4 -3 6 9
Domain 1 3 4
Range 2 -4
Is this a function – why or why not?

11. State whether the function is discrete or continuous.
At an ice sculpting competition, each sculpture’s height was measured to make sure that it was within the regulated height range of 0 to 6 feet. The measurements were as follows: Team 1, 4 feet;; Team 2, 4.5 feet; Team 3, 3.2 feet; Team 4, 5.1; Team 5, 4.8.
Make a table Determine the domain and range of the function Write the data as a set of ordered pairs. Then graph the data data.
State whether the function is discrete or continuous.

12. Equations as Functions
-3x + y = 8
Y = 8 + 3y
You can check
If it is a function
Using the vertical
Line test x y

13. Discrete vs. continuous
Discrete Continuous
Use the vertical line test to check if it is a function.

14. Function notation
F(x) = -4x + 7
F(2) F(-3) +1

15. h(t) = -16 𝑡 t +2
h(4)
2[h(g)]

16. Assignment Chapter Test – Thursday Pp 44-46; 9-20, 40, 42-60

17. Review

18. You identified functions and found function values.
Identify and interpret key features of the graphs of functions.

19. Linear v. Non-Linear Linear Graph that is a straight line. Non-Linear
Graph that is not a straight line.

20. Intercepts: Graph touches an axis
X-intercepts
The x-coordinate of the point at which a graph intersects the x-axis.
Y-intercepts
The y-coordinate of the point at which a graph intersects the y-axis.

21. Each half of the graph on either side of the line matches exactly.
Line of Symmetry
Each half of the graph on either side of the line matches exactly.

22. End Behavior

23. Extrema: Relatively high/low points
Relative Minimum
Relative Maximum

24. Where the graph lies below the x-axis.
Positive v. Negative
Positive
Where the graph lies above the x-axis.
Negative
Where the graph lies below the x-axis.

25. Increasing v. Decreasing
Where the graph goes up.
Decreasing
Where the graph goes down.

26. Describe/ label the following features of the function below:
Linear or Non-Linear? non-linear
x-intercept and y-intercepts?
x=7.2 and y=30
Line of symmetry? none
Positive/ negative?
positive: 0 < t < 7.2
negative: t > 7.2 minutes
Increasing/ decreasing?
increasing: t < 1, 4 < t < 6
decreasing: 1 < t < 4, t > 6
Extrema?
min: t = 4
max: t = 1 and t = 6
End behavior?
As x increases, y decreases.
As x decreases, y decreases.

27. Describe/ label the following features of the function below:
Non-linear
Linear or Non-Linear?
x-intercept and y-intercepts?
x=5.5 and y=80
Line of symmetry?
Positive/ negative?
Positive: between x = 0 and x = 5.5
Negative: for about x > 5.5
Increasing/ decreasing?
Increasing: between x = 1 and x = 4
Decreasing:for x < 1 and x > 4
Extrema?
Maximum: at about x = 4
Minimum: at about x = 1
End behavior?
As x increases, y decreases.
As x decreases, y increases.
None

29. Activity
Draw a graph using at least 3 of the features discussed today.
In complete sentences on the back of the graph, explain how the three terms are demonstrated in the graph you drew.