4. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Learning Goals:
I can determine the domain and range of a relation.
I can determine if a relation is a function

5. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
So far, we have seen mathematical relationships written like this:
y = 3x + 1
y = 2x2 -2
y = x2
y = 5x
Etc, etc.
These examples are relations: They are rules describing the relationship between the dependent and independent variables.
A relation is a connection (or relationship) between two sets of numbers, such as height vs. time or cost vs. weight
The Dependent Variable is:
The Independent Variable is:

6. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example: The height, h, of an object thrown up in the air is dependent on the time, t. “h” is dependent on “t”, therefore h is the dependent variable and t is the independent variable.

7. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
These examples represent function notation and are read as, “ f of x”, or “f at x”.

8. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Function notation represents a relation where there is only one unique value of the function (f) for any value of x.
In other words, each x-value (independent variable) has only one y-value (dependent variable)

9. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
How do you know whether something is a function?
If you put in a value for “x” and there is only one value for “y” it is a function.
If you put in a value for “x” and get more than one value for “y”, it is not a function.

10. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example:
INPUT
OUTPUT
INPUT
OUTPUT
Camary
Rav 4
Yaris
Prius
Camary
Venza
Rav 4
Sienna
Yaris
Corolla
Prius
Toyota
Toyota

11. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
A function can be represented by:
A Table of Values
A Set of Ordered Pairs
A Mapping Diagram
A Graph
An Equation

12. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Table of Values: It is a function if each x-value only corresponds to one y-value x y -2 3 -1 2 1 x y 1 5 3 6 7 8 2

13. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Ordered Pairs: It is a function if for each x-value there is only one y-value
f = {(1,-4), (2,5), (8, 9), (0, 6)}
g = {(1, -3), (2, -3), (3, 0), (2, 0)}

14. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Mapping Diagram: It is a function if the x-value points to only one y-value y 1 4 7 10 11 8 9 x y x 1 -1 1 2 3 4

15. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Graph: It is a function if it passes the vertical line test.
Vertical Line Test: Draw a vertical line anywhere on a graph. If the line crosses the graph more than once it is not a function.

16. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Equation: Anything in the form y = mx + b is a function. Anything in the form
y = ax2+ bx + c is a function. To check anything else, graph it!

17. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Determine whether the following relations are functions or not
a) y = 2x b) y = 2x c) x2 + y2 = 4

18. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Domain: The set of all the input values that are defined for a function. (Formerly referred to as the x-values or the independent variable.) Written from smallest to largest number.
Range: The set of all the output values for the function. Can be determined by subbing in the values from the domain. (Formerly referred to as the y-values or the dependent variable.) Also written from smallest to largest number.

19. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping

20. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example: Write the domain and range for this function using set notation. x y 1 5 3 6 7 8 2

21. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example: Write the domain and range for this function using set notation.
f = {(1,-4), (2,5), (8, 9), (0, 6)}

22. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example: Write the domain and range for this function using set notation. 1 4 7 10 11 8 9 x y

23. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Example: Write the domain and range for this function using set notation.

24. Lesson 2: Relations and Functions, Domain and Range and Mapping
Unit 1: Functions
Lesson 2: Relations and Functions, Domain and Range and Mapping
Practice
Page 12 #1, 2ac, 3ace, 5abcd, 6abc, 8, 10, 11ab
Page 22 #5-7