Math Functions and Relations, what makes them different and how to Find the Domain and Range.

In math, a relation is just a set of ordered pairs. Note: { } are the symbol for "set"

Some Examples of Relations include

{ (0,1) , (55,22), (3,-50) }
{ (0, 1) , (5, 2), (-3, 9) }
{ (-1,7) , (1, 7), (33, 7), (32, 7) }

A relation is just a set of ordered pairs. There is absolutely nothing special at all about the numbers that are in a relation. In other words, any bunch of numbers is a relation so long as these numbers come in pairs.

The domain and range of a relation

The domain is the set of all the first numbers of the ordered pairs . In other words, the domain is all of the x-values.

The range is the set of the second numbers in each pair, or the y-values.

Examples of the Domain and Range

Examples of the domain and range of a relation.
Picture of Domain and Range

In the relation above the domain is { 0, 3, 90 }

And the range is { 1, 22, 34 }

Example two of the domain and range of a relation

In the relation above,

Practice Identifying Domain and Range

What is the domain and range of the following relation?
{ (-1,2), (2, 51), (1, 3), (8, 22), (9, 51) }

Answer

What is the domain and range of the following relation
{ (-5,6), (21, -51), (11, 93), (81, 202), (19, 51) }

Answer

What is the domain and range of the following relation?

Answer

Interactive Relation

As the ball drops, you can see the relation of the ball's position and time.

The general formula to express this relation is

f(time)= position

Try changing the speed of ball's position. How does the speed effect the relation.

See this demonstration by itself(Easier to see entire demonstration)

Functions |Relations | Evaluating Functions | Vertical Line Test | Top

What makes a relation a function in Math?

Functions

are a special kind of relation .

At first glance, a function looks just like a relation. It's a set of ordered pairs such as { (0,1) , (5, 22), (11,9) }
Like a relation, a function has a domain and range made up of the x and y values of ordered pairs.

In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value.

Some people find it helpful to think of the domain and range as people in romantic relationships. If each number in the domain is a person and each number in the range is a different person, then a function is when all of the people in the domain have 1 and only 1 boyfriend/girlfriend in the range. Compare the two relations on the below. They differ by just one number, but only one is a function.

Difference between relation and function

Since relation #1 has ONLY ONE y value for each x value, this relation is a function.
On the other hand, relation #2 has TWO distinct y values '2' and '4' for the same x value of '1'. Therefore, relation #2 does not satisfy the definition of a mathematical function.

Practice Identifying Functions

Functions |Relations | Evaluating Functions | Vertical Line Test | Top

Practice Problems

Practice Problem one
Which relations below arefunctions?
Relation #1 { (-1,2), (-4,51), (1,2), (8,-51) }
Relation #2 { (13,14), (13,5) , (16,7), (18,13) }
Relation #3 { (3,90), (4,54), (6,71), (8,90) }

The Functions

Practice Problem Two

Which relations below arefunctions?

Relation #1 { (3,4), (4,5), (6,7), (8,9) }
Relation #2 { (3,4), (4,5), (6,7), (3,9) }
Relation #3 { (-3,4), (4,-5), (0,0), (8,9) }
Relation #4 { (8, 11), (34,5), (6,17), (8,19) }
The Functions

Practice Problem Three) For the following relation to be a function, X can not be what values?

{ (8, 11), (34,5), (6,17), (X ,22) }

Answer

Practice Problem Four) For the relation below to be a function, X cannot be what values?

{ (12, 13), (-11, 22), (33, 101), (X ,22) }

Answer

Practice Problem Five) For the relation below to be a function, X cannot be what values?

{ (12,14), (13,5) , (-2,7), (X,13) }

Answer

Math Functions, Relations, Domain & Range

The domain and range of a relation

Examples of the Domain and Range

Functions

Practice Identifying Functions