This activity focuses on functions that are piecewise linear, like the graphs generated below:
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Many phenomena cannot be described by a
single linear function, but can be described by functions
that are linear over intervals. For example:
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| A group of bikers rode
at a high speed during the first part of a trip, then continued
at a slower pace.
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| By law, after
8 hours of work per day, every hour is considered overtime;
employers must pay at least 25% more for the first two hours
of overtime and at least 50% more for additional hours.
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| The Flash cellular phone company
charges 5 cents per minute during the day and 2 cents per minute
after 8 pm.
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Investigate a real-life phenomenon that
can be described using functions on intervals
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Consider real-life phenomena that can be described
(exactly or approximately) using functions on intervals.
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Choose such a phenomenon and collect the relevant data (by
measurements, or from papers, books, or the Internet).
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Construct appropriate functions, raise questions
that come naturally with regard to the phenomena you
are describing, and explain whether and how
these questions can be answered using various representations
of your functions.
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