Introduction to FunctionsGiven 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 4measured the temperature of a sample of water that was heated for 10minutes, with an initial temperature of 5°Cand a constant rate of change of 2°C per minute. The formula we derived was T(m)52m=+=+, where mrepresent the number of minutes the water has been heated and Trepresents the corresponding Celsius temperature at that time. This formula certainly represents temperature Tas a function of time m. If the value for mis known, the value for Tis uniquely determined. For example, the statement T(4)13=means that after 4minutes the temperature is 13 C°, and the point (4,13)will be on the graph of this function.
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