A set of ordered pairs is called a __________.

A set of ordered pairs is called a relation.

A ________ is a set of ordered pairs in which no two ordered pairs have the same first

coordinate and different second coordinates.

A function is a set of ordered pairs in which no two ordered pairs have the same first

coordinate and different second coordinates.

The ________ of a function is the set of all the _____

coordinates of the ordered pairs.

The domain of a function is the set of all the first (x) coordinates

of the ordered pairs.

The ________ of a function is the set of all the ______

coordinates.

The range of a function is the set of all the second (y) coordinates.

The domain is the _____variable.

The domain is the x variable.

The range is the _____ variable.

The range is the y variable.

Functional Notation

f ( x)

Vertical Line Test for Functions

• A graph is the graph of a function if and only if no vertical line intersects the graph at more than one point.

Increasing, Decreasing and Constant Functions

If a and b are elements of an interval I that is a subset of the domain of a function f, then

Increasing, Decreasing and Constant Functions

If a and b are elements of an interval I that is a subset of the domain of a function f, then

• f is increasing on I if f(a) < f(b) whenever a < b.

Increasing, Decreasing and Constant Functions

If a and b are elements of an interval I that is a subset of the domain of a function f, then

• f is increasing on I if f(a) < f(b) whenever a < b.

• f is decreasing on I is f(a) > f(b) whenever a > b.

Increasing, Decreasing and Constant Functions

If a and b are elements of an interval I that is a subset of the domain of a function f, then

• f is increasing on I if f(a) < f(b) whenever a < b.

• f is decreasing on I is f(a) > f(b) whenever a > b.

• f is constant on I if f(a) = f(b) for all a and b.

Horizontal Line Test

• If every horizontal line intersects the graph of a function at most once, then the graph is the graph of a one to one function.

Functions whose graphs can be drawn without

lifting the pencil off the paper are called

continuous functions.

Functions with holes, breaks, or gaps have

discontinuities.

Greatest Integer Function