1. _________ and __________
Unit 4 - Relations and Functions

2. Unit 4 - Relations and Functions
Some Definitions-
A _________ between two variables ____
and _____ is a set of __________ pairs
An ordered pair consists of an x and y
____________
A relation may be viewed as ordered _______, __________ design, _________, ________, or written in sentences
x-values are _______, _______, ___________ variable
y-values are __________ __________, __________ variable
Unit 4 - Relations and Functions

3. Example 1: What makes this a relation?
What is the domain?
What is the range?
Unit 4 - Relations and Functions

4. Example 2 – Is this a relation?4 –5 9 –1
Input –2 7
Output
What is the domain?
{4, -5, 0, 9, -1}
What is the range?
{-2, 7}
Unit 4 - Relations and Functions

5. Is a relation a function?
What is a function?
According to a textbook, “a function is…a relation in which ________ ________is paired with exactly ______ __________”
Unit 4 - Relations and Functions 5 5

6. Is a relation a function?
Focus on the x-coordinates, when given a relation
If the set of ordered pairs has __________ x-coordinates,
it ______ A function
it is _________ a function
Y-coordinates have no bearing in determining functions
Unit 4 - Relations and Functions

7. Unit 4 - Relations and Functions
Example 3
:00
Is this a relation?
Is this a function?
Hint: Look only at the x-coordinates
Unit 4 - Relations and Functions

8. Unit 4 - Relations and Functions
:40
Example 4
Is this a function?
Hint: Look only at the x-coordinates
Is this still a relation?
Unit 4 - Relations and Functions

9. Which relation mapping represents a function?
:40
Example 5
Which relation mapping represents a function?
Choice One Choice Two 3 1 –1 2 2 –1 3 –2
Unit 4 - Relations and Functions

10. Unit 4 - Relations and Functions
Example 6
Which relation mapping represents a function?
A B.
Unit 4 - Relations and Functions

11. Unit 4 - Relations and Functions
Example 7
Which situation represents a function?
a. The items in a store to their prices on a certain date
b. Types of fruits to their colors
A fruit, such as an apple, from the domain would be associated with more than one color, such as red and green. The relation from types of fruits to their colors is not a function.
There is only one price for each different item on a certain date. The relation from items to price makes it a function.
Unit 4 - Relations and Functions

12. Unit 4 - Relations and Functions
Vertical Line Test
Vertical Line Test: a relation is a function if a __________ __________drawn through its graph, passes through only _______ __________. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function
Unit 4 - Relations and Functions

13. Would this graph be a function?
Vertical Line Test
Would this graph be a function?
YES
Unit 4 - Relations and Functions

14. Would this graph be a function?
Vertical Line Test
Would this graph be a function? NO
Unit 4 - Relations and Functions

15. Unit 4 - Relations and Functions
Is the following function discrete or continuous? What is the Domain? What is the Range?
Unit 4 - Relations and Functions

16. Unit 4 - Relations and Functions
Is the following function discrete or continuous? What is the Domain? What is the Range?
Unit 4 - Relations and Functions

17. Unit 4 - Relations and Functions
Is the following function discrete or continuous? What is the Domain? What is the Range?
Unit 4 - Relations and Functions

18. Unit 4 - Relations and Functions
Is the following function discrete or continuous? What is the Domain? What is the Range?
Unit 4 - Relations and Functions

19. Unit 4 - Relations and Functions
Domain and Range in Real Life
The number of shoes in x pairs of shoes can be expressed by the equation y = 2x.
What is the independent variable?
What is the dependent variable?
Unit 4 - Relations and Functions 19

20. Unit 4 - Relations and Functions
Domain and Range in Real Life
Mr. Landry is driving to his hometown. It takes four hours to get there. The distance he travels at any time, t, is represented by the function d = 55t (his average speed is 55mph.
What is the independent variable?
What is the dependent variable?
Unit 4 - Relations and Functions 20

21. Unit 4 - Relations and Functions
Domain and Range in Real Life
Johnny bought at most 10 tickets to a concert for him and his friends. The cost of each ticket was $12.50.
Complete the table below to list the possible domain and range. 1 2 3
12.50
25.00
37.50
What is the independent variable?
What is the dependent variable?
Unit 4 - Relations and Functions

22. Unit 4 - Relations and Functions
Domain and Range in Real Life
Pete’s Pizza Parlor charges $5 for a large pizza with no toppings. They charge an additional $1.50 for each of their 5 specialty toppings (tax is included in the price).
Jorge went to pick up his order. They said his total bill was $9.50. Could this be correct? Why or why not?
Susan went to pick up her order. They said she owed $ Could this be correct? Why or why not?
Unit 4 - Relations and Functions

23. Unit 4 - Relations and Functions
Domain and Range in Real Life
Pete’s Pizza Parlor charges $5 for a large pizza with no toppings. They charge an additional $1.50 for each of their 5 specialty toppings (tax is included in the price).
What is the independent variable?
What is the dependent variable?
Unit 4 - Relations and Functions 23

24. Unit 4 - Relations and Functions
Function Notation
f(x) means function of x and is read “f of x.”
f(x) = 2x + 1 is written in function notation.
The notation f(1) means to replace x with 1 resulting in the function value.
f(1) = 2x + 1
f(1) = 2(1) + 1
f(1) = 3
Unit 4 - Relations and Functions

25. Unit 4 - Relations and Functions
Function Notation
Given g(x) = x2 – 3, find g(-2) .
g(-2) = x2 – 3
g(-2) = (-2)2 – 3
g(-2) = 1
Unit 4 - Relations and Functions

26. 1-6 Relations and Functions
Function Notation
Given f(x) = , the following.
a. f(3)
f(3) = 2x2 – 3x
f(3) = 2(3)2 – 3(3)
f(3) = 2(9) - 9
f(3) = 9
12/3/2018 8:14 AM
1-6 Relations and Functions