Vocabulary:RelationFunction DomainRangeIndependent VariableDependent VariableInput valuesOutput valuesDiscreteContinuous

FUNCTIONS

This is read as the set f of ordered pairs.

The set of all first coordinates of a relationis called the domain of the relation.

For f = { (1, 7), (2, 14), (3, 21), (4, 28) },The domain is {1, 2, 3, 4}.

For f = { (1, 7), (2, 14), (3, 21), (4, 28) },The range is {7, 14, 21, 28}.

The set of all second coordinates is called the range.

f = { (1, 7), (2, 14), (3, 21), (4, 28) }

This relation relates y to x;f relates y to x.

For f = { (1, 7), (2, 14), (3, 21), (4, 28) }.Is it a FUNction??

We say that y depends upon the value of x.

So, y is called the dependent variable andx is called the independent variable.

x is also called the input value and y is called the output value.

What we’ve learned so far…

x y OR f(x)

Domain Range

Independent variable

Dependent variable

Input values Output values

Find the domain and range of the following relations, afterwards note

whether each IS or IS NOT a function.1) { (2, 9), (5, 9), (8, 9), (11, 9) } 2) { (4, 5), (8, 1), (-2, 0), (4, 13) }

3) { (1, 5), (2, 5), (3, 5), (4, 5) } 4) { (-10, 5), (-6, 3), (-1, 0), (3, 5) }

Sometimes a relation can be representedby a graph.

You can easily determine the domain and range of a relation given a discrete graph.

y

x

A

BC

DE

First, write the coordinates for each point.

A graph that contains only points is called discrete.A graph that contains lines/curves is called continuous.

A ( -2, 4)

B ( 0, 8)

C ( 3, 5)

D ( 3, -2)

E ( -4, 0)

So the domain is (all the x-values):

And the range is (all the y-values):

D = { -2, 0, 3, -4 }

R = { 4, 8, 5, -2, 0 }

Sometimes a relation can be representedby a table of values.

The relation f = { (2, 5), (4, -6), (3, 6), (2, 8) }

can be written as a table of values.

x y

2 5

4 -6

3 6

2 8

x 2 4 3 2

y 5 -6 6 8

VERTICAL

H O R I Z O N T A L

Remember, the x-values represent domain values of the relation and the y-values represent range values.

Sometimes a relation can be representedin a diagram called a mapping.

The relation f = { (2, 5), (3, 7), (4, 9), (5, 11) }

is being diagramed inmapping below.

x y

2

3

4

5

5

7

9

11

The arrows in a mappingrelate y to x. This is just another way torepresent ordered pairs:(2, 5), (3, 7), (4, 9), (5, 11).

Remember:Domain x-valuesRange y-values

Find the domain and range of the following relations

Label each as function or not a function.1)

{ (1,1), (2,2), (3,3), (4,4) }

2) 3) 4)

5) 6)

{ (2,1), (4,8), (0,6), (0,9) }

7) 8)

Name_________________________

x y

3 -1

4 0

5 1

6 2

x 3 1 -3 0

y 5 8 5 -1

1

3

7

-8

0

-2

9

8

7

6

5

0

1

2

3