FUNCTIONS
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Understanding Functions and Relations: Domain, Range, and Types, Lecture notes of Mathematics
An introduction to functions and relations, explaining the concepts of domain and range, and discussing the different types of relations: one-to-one, one-to-many, many-to-one, and many-to-many. It also covers how to identify functions using mapping diagrams and the vertical line test.
Typology: Lecture notes
2019/2020
1 / 16
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Understanding Functions and Relations: Domain, Range, and Types and more Lecture notes Mathematics in PDF only on Docsity!
FUNCTIONS
It is a set of ordered pairs.
It is defined as a set of inputs and outputs
RELATION
DOMAIN - A set of INPUT values (First element, Independent Variable, Argument)
RANGE - A set of OUTPUT values (Second Element, Dependent Variable, Value of function)
FUNCTIONS
It relates an INPUT to an OUTPUT.
It is a relation in which each element of the domain corresponds to EXACTLY ONE element of the range.
Each input value (X) has ONLY ONE output value (Y).
INPUT FUNCTION OUTPUT
ORDERED PAIRS
- It is pair of numbers/letters/words that go together. They are written within a set of parentheses and separated by a comma.
WRITING THE THREE EXAMPLES IN THE PREVIOUS SLIDE IN ORDERED PAIRS
**1. (50, 55), (40, 45), (30, 35), (20, 25) FUNCTION
- (A, E), (B, F), (C, G), (C, H), (D, H) NOT A FUNCTION
- (1, A), (2, B), (3, C), (4, C) FUNCTION**
HOW TO DETERMINE IF THE SET OF ORDERED PAIRS IS A FUNCTION
**1. (4, 8), (3, 6), (5, 10), (2, 7)
- as we can see, the first elements, or the domains, didn’t have any repeating values. Therefore, this example is a FUNCTION
- (10, 8), (11, 29), (17, 9), (10, 5)
- as for this example, we can see that the first elements or the domains have repeated values (10). Therefore, this example is NOT A FUNCTION
- (5, 8), (17, 9), (3, 8), (10, 9)
- as for this example, we can see that the second element, or the range, has repeated values, whereas the first element, or domain, didn’t have any repeating values. Therefore, this example is still a FUNCTION**
TYPES OF RELATION
ONE-TO-ONE RELATION
ONE-TO-MANY RELATION
MANY-TO-ONE RELATION
MANY-TO-MANY RELATION
MANY-TO-ONE RELATION
- A domain (X) can have two or more values of range (Y).
- The values of (X) can be repeated.
G
O
T
1 6 4 7
X Y
- This relation is NOT A FUNCTION. Because there was a repetition of a domain (X).
MANY-TO-MANY RELATION
- The domain (X) and the range (Y) have repeated values.
- Both Value of (X) and (Y) are repeated
- This relation is NOT A FUNCTION. Because the values of X (DOMAIN) are repeated.
B
T
S
A
R
M
Y
X Y
MANY-TO-MANY RELATION
A
C
E
B
D
F
X Y
5 4 2 1
0 6 2 7
X Y
ONE-TO-ONE RELATION
1
4
MANY-TO-ONE RELATION
9 7
1
ONE-TO-MANY RELATION
X Y X Y
NOT A FUNCTION
FUNCTION
FUNCTION
NOT A FUNCTION
X Y
X - 3 - 2 - 1 0 1 2 3 4
Y 6 0 - 4 - 6 - 6 - 4 0 6
PLOT THE POINTS CONNECT THE POINTS
HOW TO DETERMINE THE DOMAIN AND THE RANGE OF A FUNCTION THROUGH THE GRAPH
The x-value at the farthest left point is at x=-2. The x-value at this point is at 2. There are no breaks in the graph going from left to right which means it’s continuous from -2 to 2.
The DOMAIN is [-2, 2]
Now look at the furthest point down on the graph or the bottom of the graph. The y-value at this point is y=1. Now look at how far up the graph goes or the top of the graph. We need to look at the y-value of this point which is at y=5. There are no breaks in the graph going from top to bottom which means it’s continuous.
The RANGE is [1, 5]
Assume the graph does not extend beyond the graph shown.