1. Discrete and Continuous Functions

2. Discrete Function
The graph of a discrete function consists of separate points.

3. Continuous Function
The graph of a continuous function is unbroken.

4. Domain and Range
Domain (-∞,∞)
Range [0,∞)
{y: y>0}

5. Domain and Range
Domain [0,∞)
Range [0,∞)
{y: y>0}

6. Is this graph a function?
Yes, there is only one y for every x. Or only one output for each input.

7. 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.

8. Is this graph a function?
Yes, every vertical line intersects the graph 0 or 1 times.

9. 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).

10. 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?