Discrete and Continuous
Functions
Discrete Function
The graph of a discrete function
consists of separate points.
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
Continuous Function
The graph of a continuous function
is unbroken.
3.5
3
2.5
2
1.5
1
0.5
0
1
2
3
4
Domain and Range
1.2
Domain (-∞,∞)
1
Range [0,∞)
{y: y>0}
0.8
0.6
0.4
0.2
0
-1.5
-1
-0.5
0
0.5
1
1.5
Domain and Range
2.5
Domain [0,∞)
2
Range [0,∞)
{y: y>0}
1.5
1
0.5
0
0
1
2
3
4
5
Is this graph a function?
2.5
Yes, there is
only one y for
every x. Or
only one
output for
each input.
2
1.5
1
0.5
0
0
1
2
3
4
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?
3.5
Yes, every
vertical line
intersects the
graph 0 or 1
times.
3
2.5
2
1.5
1
0.5
0
1
2
3
4
Is this graph a function?
5
4
3
2
1
0
-1
-2
0
2
4
6
8
No, the
vertical line
intersects the
graph twice.
This means
that at least
one input (x)
has more than
one output
(y).
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?