Math 121

Section 1.4 Functions

Key Terms

Relation: A set of ordered pairs

Domain: The set of all x-values or first coordinates in a relation.

Range: The set of all y-values or second coordinates in a relation.

Example: Find the domain and range of the relation {(1,2),(2,4),(3,6),(6,7),(8,9)}

Domain: {1,2,3,6,8}

Range: {2,4,6,7,9}

Function: A relation where every element in the domain is paired with exactly one element in the range.

Examples

Given the domain and range of each relation and determine if the relation is a function.

1) {(1,2),(3,4),(5,9),(6,5),(9.9)}

Answer: Domain: {1,3,5,6,9}

Range: {2,4,9,5,9}

This is a function

2) {(1,1),(2,3),(2,5),(4,6),(6,8)}

Answer: Domain: {1,2,4,6}

Range: {1,3,5,6,8}

This is not a function because 2 is paired with two values 3 and 5

3)

Domain: {Greg, John, Bob, Mike},Range={Jane, Jill, Beth, Carol, Molly}

This is not a function. (Mike is paired with Carol and Molly)

Vertical Line Test

If a vertical line can be drawn so that it intersects the graph a relation 2 or more times, then the relation is not a function.

Examples

1) Use the graph to determine if the relation is a function, and give the domain and range.

This is not a function, since the relation fails the vertical line test.

Domain: , Range:

2) Use the graph to determine if the relation is a function, and give the domain and range.

This is a function since every vertical line on the graph would intersect the relation only once. Domain: : Range:

Function Notation

Example of functions

Given the three functions above, find the following values.

1) Find

2) Find

3) Find

4) Find

5) Find

6) Find