Notes: Relations and Functions
Name:
(Page 72)
Date:
Period:
A ________________ is a ___________ or _____________ of input values with output values.
The set of input values is the ______________.
The set of output values is the _____________.
Relations can be represented in the following ways.
Ordered Pairs
Table
(-2, 2)
x
-2
-2
0
3
(-2, - 2)
( 0, 1)
Graph
Mapping
Input
y
2
-2
1
1
( 3, 1)
output
-2
2
0
-2
3
1
Consider the relation given by the following ordered pairs (-2, 1), ( -1, -4), ( 0, 5), ( 1, -3), (3, 5).
a. Identify the domain and range. _____________________________________________
b. Represent the relation using a graph and a mapping diagram.
y
mapping
x
______________________________________________________________________________
A _____________ is a relation for which each ____________ has exactly one ______________.
Consider the examples we have already used. Is either of them a function? Why or why not?
input
output
input
output
-2
2
-2
-4
0
-2
-1
-3
3
1
0
1
1
5
3
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.
Discrete and Continuous Functions The graph of a ____________function consists of separate points.
The graph of a ______________ function is unbroken.
Using the vertical line test, determine whether or not the following graphs are graphs of functions.
Then, identify the domain, range and whether the graph is discrete or continuous.
Function? yes
or
no
Function? yes
or
no
Function? yes
or
no
domain ____________
domain _____________
domain _____________
range ______________
range _______________
range_______________
discrete or continuous
discrete or continuous
discrete or continuous
Function? yes
Function? yes
or
no
or
no
Function? yes
or
no
domain ____________
domain _____________
domain _____________
range ______________
range _______________
range_______________
Set notation
{x|x  3} This is pronounced as "the set of all x, such that x is less than 3.