The sum of two linear functions is a linear function. But
their product (when you multiply two linear functions) is a quadratic
function. This activity helps you examine functions constructed
by multiplying linear functions and explore how the properties of
the "parents" (the linear functions) affect the properties of
the "child" (the product function).
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The dynamic figure below presents graphic examples
of linear functions and of their product function.
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The activity helps you investigate systematically the properties of products of linear functions in various representations
(graphs, value tables, and correspondence rules).
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Write an essay about products of linear functions
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Write a story, as complete as you can, about products of linear functions
and the relations between the properties of the linear functions that are
being multiplied and the properties of the product function.
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Describe the course of your investigation and indicate your preliminary conclusions,
your decisions, and mathematical justifications. What is your degree
of confidence in your conclusions and decisions? Why?
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Write also about the "Standard Product Form" and the relation between
this form and "general" products of linear functions.
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Use the tools provided to record important points for discussion and interesting or problematic
cases.
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After a preliminary investigation of the products of linear functions, you
may want to turn to some of the tasks and exercises, which will help
you verify and apply what you have learned and perhaps suggest
other directions for investigation.
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