1. Notes from a PPT: Functions vs. Relations / Domain & Range
Coordinate Algebra
Agenda:
Notes from a PPT: Functions vs. Relations / Domain & Range
Learning Target:
Students can define a relation and explain the difference between a relation and a function.
Students can determine the domain and range of relations and functions.
Standard: MCC9-12.F.IF.1 and 2

2. Functions vs. Relations

3. Relation A relation is simply a set of ordered pairs.
The set of all first values (x- values) is the domain. The set of all second values (y-values) is the range.

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. 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

8. function Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)}
Is the following relation a function?
Example 1:
{(3, 2), (4, 3), (5, 4), (6, 5)}
function

9. Is the following relation a function?
Example 2:
function

10. Is the following relation a function?
Example 3:
relation

11. function Is the following relation a function? Example 4:
( x, y) = (student’s name, shirt color)
function

12. Is the following relation a function?
Example 5: Red Graph
relation

13. function Is the following relation a function? Jacob Angela Nick Honda
Example 6
Jacob
Angela
Nick
Greg
Tayla
Trevor
Honda
Toyota
Ford
function

14. function A person’s cell phone number versus their name.
Is the following relation a function?
Example 7
A person’s cell phone number versus their name.
function

15. Only list repeated values once Put in order from least to greatest
Domain and Range
Only list repeated values once
Put in order from least to greatest

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

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

18. What are the Domain and Range?
All Reals
All Reals

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

20. Functions Practice worksheet
Homework
Functions Practice worksheet