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Introduction to Functions
Given a set of inputs (called the independent set) and a corresponding set of outputs (called the dependent set).
A
functional relationship exists between these two sets if each input value determines only one value for the output.
The formula we developed in class in our study of
The Rule of 4
measured the temperature of a sample of water that was
heated for
10
minutes, with an initial temperature of
5°C
and a constant rate of change of
2°
C per minute.
The formula we
derived was
T(m)
5
2m
= +
= +
= +
= +
, where
m
represent the number of minutes the water has been heated and
T
represents the
corresponding Celsius temperature at that time.
This formula certainly represents temperature
T
as a function of time
m
.
If
the value for
m
is known, the value for
T
is uniquely determined.
For example, the statement
T(4)
13
=
means that after
4
minutes the temperature is
13 C
°
, and the point
(4,13)
will be on the graph of this function.
As a second example, consider the statement “Your grade for College Algebra is a function of your point total at the end of

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