Set of all x-values.
Range
Domain
What is a relation?
A rule that relates values from a set of values (called the domain) to a second set of values (called the range).
It is NOT the connection between the set of ordered pairs (x,y).
Set of all y-values.
The connection between the set of ordered pairs.
Relation
Function
Determine the DOMAIN and RANGE of the following ordered pairs.
f = {(a,1) , (b,2) , (c,3) , (d,4)}
DOMAIN : (1,2,3,4) RANGE : (a,b,c,d)
DOMAIN : (a,b,c,d) RANGE : (1,2,3,4)
f = {(1,3) , (1,4) , (2,5) , (2,6) , (3,7)}
DOMAIN : (1,2,3) RANGE : (3,4,5,6,7)
DOMAIN : (3,4,5,6,7) RANGE : (1,2,3)
It states that x-values from domain can respond to only one y-value.
One-to-One
One-to-Many
Many-to-One
Many-to-Many
It states that single x-value corresponds to two or more y-values.
It is a combination of one-to-many and many-to one.
It states that every value from a set of values (domain) corresponds to their unique second set of values (range).
Determine the types of the following relation.
A = {(2,1) , (2,3) , (2,5)}
A = {(4,5) , (1,6) , (4,-7) , (2,6) , (4,8) , (3,6)}
What is a function?
Set of domains.
A relation where each element in the domain is related to only one value in the range by some rule.
All functions are relations, and all relations are also functions.
Many-to-Many relation is NOT a function.
One-to-One relation is a Function.
Many-to-One relation is NOT a function.
One-to-Many relation is a function.
All functions are relations but not all relation are functions.
Vertical line test is a visual way to determine if a curve is a graph of a function.
