(1)32 mpg(2)8 mpg(3)16 mpg

(A)

(C)

(B)

The values that make up the set of independent values are the domain

The values that make up the set of dependent values are the range.

State the domain and range from the 4 examples of relations given.

Transitive:If a = b and b = c then a = c

Identity: a + 0 = a, a • 1 = a

Commutative:a + b = b + a, a • b = b • a

Associative:(a + b) + c = a + (b + c)(a • b) • c = a • (b • c)

Distributive: a(b + c) = ab + aca(b - c) = ab - ac

if a is positive

if a is negative

A Relation maps a value from the domain to the range. A Relation is a set of ordered pairs.

The most common types of relations in algebra map subsets of real numbers to other subsets of real numbers.

Domain Range

3 π

11 - 2

1.618 2.718

This is often referred to as a diagrammatic representation of a relation. Note that each element in the domain is connect to it’s respective range element by the arrow.

The relation is the year and the cost of a first class stamp.

The relation is the weight of an animal and the beats per minute of it’s heart.

The relation is the time of the day and the intensity of the sun light.

The relation is a number and it’s square.

If a relation has the additional characteristic that each element of the domain is mapped to one and only one element of the range then we call the relation a Function.

x

DOMAIN

y

RANGE

f

FUNCTION CONCEPT

x

DOMAIN

y1

y2

RANGE

R

NOT A FUNCTION

y

RANGE

f

FUNCTION CONCEPT

x1

DOMAIN

x2

SymbolicSymbolic

x,y y 2x or

y 2x

X Y

1 2

5 10

-1 -2

3 6

• GraphicalGraphical

• NumericNumeric

• VerbalVerbalThe cost is twice the original amount.

A truly excellent notation. It is concise and useful.

y f x

y f x • Output Value• Member of the Range• Dependent Variable

These are all equivalent names for the y.

• Input Value• Member of the Domain• Independent Variable

These are all equivalent names for the x.

Name of the function

The f notation

f x x 1

f 2 2 1