1. Lesson 8.1 Relations and Functions
Essential Question: How do you represent relations and functions?

2. Before we start… Label the coordinate plane: x-axis y-axis Origin
Quadrants I - IV

3. Before we start…
ITunes is having a major sale on music right now. Songs cost $0.50 each!
What is your cost if you buy…
4 songs?
8 songs?
12 songs?
20 songs?
Do you notice a pattern?

4. What is a relation? A set of ordered pairs
Relates an input and an output

5. What is an…
input? the x values
output? the y values

6. What are… Domain? Range? Set of all possible input values (x)
Set of all possible output values (y)

7. The table below shows the ages and lengths of five alligators
The table below shows the ages and lengths of five alligators. Identify the domain and range of the relation.
Age (years), x 2 4 5 7
Length (inches), y 32 59 65 69 96

8. The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the function.
Input (gallons) 10 12 13 17
Output (dollars)
19.99
23.99
25.99
33.98

9. Identify the domain and range of the function.
Input 1 2 4
Output 5

10. Identify the domain and range
Input
Output 5 1 7 2 15 3 44

11. Identify domain and range

12. Identify domain and range
Input
Output 6 5 12 7 21 10 42 17

13. How do you represent relations and functions?
Ordered pairs
Tables
Graphs
Mapping diagrams

14. Mapping Diagrams A function may be represented by a mapping diagram.
An output may be paired with more than one input, but no input is paired with more than one output.

15. Represent the relation −1,1 , 2,0 , 3,1 , 3,2 , 4,5 as indicated. a
Represent the relation −1,1 , 2,0 , 3,1 , 3,2 , 4,5 as indicated. a. A graph b. A mapping diagram

16. Represent the relation 0,3 , 1,2 , 2,−1 , 4,4 , 5,4 as indicated. a
Represent the relation 0,3 , 1,2 , 2,−1 , 4,4 , 5,4 as indicated. a. A graph b. A mapping diagram

17. What is a function? A special relation
Each input has exactly one output
Each x has one y

18. How does a function work?
A function rule assigns each number in the domain to exactly one number in the range.

19. Ways to Look at a Function
Verbal Rule
The output is 3 more than the input.
Equation
y = x + 3
Table

20. How do I identify a function?
Each input will have only ONE output.
Tables and ordered pairs can be used to identify a function.

21. Tell whether the pairing is a function

22. Tell whether the relation is a function.
Input 9 25
Output 3 -3 5 -5
Input -4 4 8
Output 32

23. Tell whether the relation is a function.
Input 3 6 9 12
Output 1 2
Input 2 4 7
Output 1 3

24. Tell whether the relation is a function.
0,2 , 1,4 , 2,6 , 3,8
−2,4 , 2,4 , 4,2 , −2,−4

25. Tell whether the relation is a function.
3,−2 , 6,1 , −3,5 , 4,1
5,1 , 5,3 , 7,1 , 8,4

26. Vertical Line Test
You can use the graph of a relation to determine whether it is a function.

28. Are these functions?

29. Is this a function?

30. Is this a function?

31. Tell whether the relation is a function
Tell whether the relation is a function. If it is, is the function linear?

32. Tell whether the relation is a function
Tell whether the relation is a function. If it is, is the function linear?

33. Tell whether the relation is a function
Tell whether the relation is a function. If it is, is the function linear?

34. How do you represent relations and functions?

35. Ticket Out the Door
Identify the domain and range of the relation. 0,0 , 1,2 , 2,4 , 3,6 , 4,8