Introduction to Functions

Objective: State the domain and range of a relation and tell whether it

is a function.

725 3)5.1(2 16)4( 2

44.1)2.1( 2 8)2( 3 001.0)1.0( 3

Functions

• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.

Functions

• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.

• The first variable (usually x) is called the domain of the function.

• The second variable (usually y) is called the range of the function.

Functions

• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.

• The first variable (usually x) is called the domain of the function.

• The second variable (usually y) is called the range of the function.

• For every value of x, there is one and only one value for y.

Example 1

Example 1

Example 1

Try This

• State whether the data in each table represents a function.

Try This

• State whether the data in each table represents a function.

yes

Try This

• State whether the data in each table represents a function.

yes yes

Try This

• State whether the data in each table represents a function.

yes yes no

Vertical Line Test

• Remember that a vertical line is a line with the equation x = c, where c is an arbitrary constant. All points on the line have the same x-coordinate. If a vertical line crosses a graph more than once, that means for that one value of x there will be more than one value for y.

Vertical Line Test

• Remember that a vertical line is a line with the equation x = c, where c is an arbitrary constant. All points on the line have the same x-coordinate. If a vertical line crosses a graph more than once, that means for that one value of x there will be more than one value for y.

• If every vertical line intersects a graph at no more than one point, then the graph represents a function.

Example 2

Definition of a Relation

• A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation.

• The domain is the set of all possible values of the first variable. The range is the set of all possible values of the second variable.

Example 4

Example 4

Try This

Try This

}2,1,0,3{ range

}5,3,2,1,3,4{domain

1 range

2domain

y

x

Function Notation

Function Notation

Example 5

Example 5

Example 6

Example 6

Homework

• Pages 108-109• 17-49 odd