Chapter 4.8: Determine if the Relation is a Function

Lesson 4.8: Function & RelationsDefinition

Function: A rule that establishes a relationship

between 2 quantities, the input and the output.

Domain: x values

Range: y values

Input: x values

Output: y values

Set Notation {1,2,3}Only write the number once, even if it repeats

Relation: Any set of ordered pairs

For every x there is exactly one y

Lesson 4.8: Determining if the relation is a function

To determine if a given relation is afunction, we use the vertical line test.

If the vertical line intersects the relation at one

point as it moves across the graph, thenthat graph is a function.If the vertical line intersects the relation

at more than one point as it moves across

the graph, then that graph is NOTa function.

Lesson 4.8: Determining if the relation is a function- Vertical Line Test

x

y

Run a vertical line across the page from left to right

Since the line only touched once, there is only one x value for every y, it is a function.

Lesson 4.8: Determining if the relation is a function- Vertical Line Test

x

y

Run a vertical line across the page from left to right

Since the line touched more than once, there is more than one x value for every y, it is a function.

Lesson 4.8: Determining if the relation is a function given a table of

values

Step 1: Graph each point

Step 2: Conduct vertical line test.

1

2

3

4

1

3

4

Input Output x y

1 1 2 3 3 3 4 4

Domain:

Range:

{1,2,3,4}

{1,3,4}

Lesson 4.8: Determining if the relation is a function given a table of values

x

y

Step 1: Graph each point

1

2

3

4

1

3

4

Input Output Step 2: Vertical Line Test

Since the line only touched once, there is only one x value for every y, it is a function.

Lesson 4.8: Determining if the relation is a function given a table of values

x

y

Step 1: Graph each point

4

1

3

4

Input Output Step 2: Vertical Line Test

Since the line touched more than once, there is more than one x value for every y, it is a function.

Lesson 4.8: Determining if the relation is a function given a table of values

Input Output

1

2

3

4

1

3

4

Input Output

4

1

3

4