Discrete and Continuous Functions

Discrete Function

The graph of a discrete function consists of separate points.

0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

Continuous Function

The graph of a continuous function is unbroken.

1 2 3 40

0.5

1

1.5

2

2.5

3

3.5

Domain and Range

-1.5 -1 -0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

Domain (-∞,∞)

Range [0,∞) {y: y>0}

Domain and Range

Domain [0,∞)

Range [0,∞) {y: y>0}

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

Is this graph a function?

Yes, there is only one y for every x. Or only one output for each input.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

Vertical Line Test

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

WHAT?????It is a function if you draw a vertical line (up and down) anywhere on the graph and it intersects the graph 0 or 1 times. NOT 2 or more.

Is this graph a function?

Yes, every vertical line intersects the graph 0 or 1 times.

1 2 3 40

0.5

1

1.5

2

2.5

3

3.5

Is this graph a function?

No, the vertical line intersects the graph twice. This means that at least one input (x) has more than one output (y).

0 1 2 3 4 5 6 7

-2

-1

0

1

2

3

4

5

What did you learn?• What are discrete and continuous

functions?• How do you determine the domain

and range of continuous functions?• How do I apply the vertical line test

to determine if a relation is a function?