1. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Learning Goals:
I can determine if a relation is a function

2. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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:

3. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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.

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

5. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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)

6. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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.

7. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Example:
INPUT
OUTPUT
INPUT
OUTPUT
Camary
Rav 4
Yaris
Prius
Camary
Venza
Rav 4
Sienna
Yaris
Corolla
Prius
Toyota
Toyota

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

9. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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

10. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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)}

11. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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

12. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Graph: It is a function if it passes the vertical line test.
Vertical Line Test: Draw a vertical line through the graph. If the line crosses the graph more than once it is not a function.

13. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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!

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

15. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
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.

16. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions

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

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

19. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation. 1 4 7 10 11 8 9 x y

20. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation.

21. Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Practice
Level 4: pg # 1 – 12, 14
Level 3: pg # 1 – 10, 14
Level 2: Pg #1-7, 14
Level 1: Pg #1 -3, 14