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The dynamic figure below shows a function in four
different presentations:
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Prepare an essay on the relations among various representations of a linear function
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Describe how changing one representation affects
the other representations. Address the following issues:
Is it possible to present a different value table
for the same function?
How can you change the value table in order to
change the slope of the graph or its points of intersection with the
axes?
Is it possible to change the correspondence rule without
changing the other representations of a function?
Examine different types of linear functions, for example
functions with a rising, falling, or level graph, and
relate the properties of the graph to properties of the numbers
that appear in the correspondence rule.
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Describe the course of your investigation,
your intermediate conclusions, your decisions, and their
mathematical justifications. In each case state what is your
level of confidence in your conclusions and why.
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Use the available tools to record important points for discussion and
interesting or problematic cases.
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Bring examples of phenomena from daily life
that can be described by linear functions.
Ask questions that
can be answered using one or more
of the functions' representations, and discuss
the pros and cons of various representations
in answering these questions.
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