Download 1.6

A relation is a pairing of input values with output
values. It can be shown as a set of ordered pairs (x,y),
where x is an input and y is an output.
The set of input values for a relation is called the domain,
and the set of output values is called the range.
Mapping Diagram
Domain
Range
A
B
C
2
Set of Ordered Pairs:
(x, y)
{(2, A), (2, B), (2, C)}
(input, output)
(domain, range)
Example 1: Identifying Domain and Range
Give the domain and range for this relation:
{(100,5), (120,5), (140,6), (160,6), (180,12)}.
List the set of ordered pairs:
{(100, 5), (120, 5), (140, 6), (160, 6), (180, 12)}
Domain: {100, 120, 140, 160, 180} The set of x-coordinates.
Range: {5, 6, 12}
The set of y-coordinates.
Suppose you are told that a person entered a word into a text
message using the numbers 6, 2, 8, and 4 on a cell phone. It would
be difficult to determine the word without seeing it because each
number can be used to enter three different letters.
However, if you are told to enter the word MATH into a text message,
you can easily determine that you use the numbers 6, 2, 8, and 4,
because each letter appears on only one numbered key.
The first coordinate is different in
{(M, 6), (A, 2), (T, 8), (H,4)} each ordered pair.
A relation in which the first coordinate is never repeated is called a
function. In a function, there is only one output for each input, so
each element of the domain is mapped to exactly one element in the
range.
Although a single input in a function cannot be mapped to
more than one output, two or more different inputs can be
mapped to the same output.
Not a function: The
relationship from number to
letter is not a function because
the domain value 2 is mapped to
the range values A, B, and C.
Function: The relationship from
letter to number is a function
because each letter in the domain
is mapped to only one number in
the range.
Example 2: Determining Whether a Relation is a
Function
Determine whether each relation is a function.
A. from the items in a store to their prices on
a certain date
There is only one price for each different item on
a certain date. The relation from items to price
makes it a function.
B. from types of fruits to their colors
A fruit, such as an apple, from the domain would
be associated with more than one color, such as
red and green. The relation from types of fruits
to their colors is not a function.
Every point on a vertical line has the same x-coordinate, so
a vertical line cannot represent a function. If a vertical line
passes through more than one point on the graph of a
relation, the relation must have more than one point with
the same x-coordinate. Therefore the relation is not a
function.
Ex 3: Use the vertical-line test to determine whether
the relation is a function. If not, identify two
points a vertical line would pass through.
This is a function. Any vertical line would
pass through only one point on the
graph.
This is not a function. A vertical line
at x = 1 would pass through (1, 1)
and (1, –2).