This activity focuses on algebraic operations
between functions, in particular
addition and subtraction.
The dynamic figure below presents examples
of operations between linear functions. You can
consider these operations to be generalizations
of operations between numbers, and you can inquire
about the properties of a function obtained
as the result of such an operation as you would in the case of
operations between numbers. For example, some
operations between numbers preserve some of the
properties of the numbers involved, others do not. The
addition of two integers always results in an integer,
but a division between integers
sometimes results in a non-integer.
|
|
The tools available for this activity
can help you study the addition and
subtraction of functions by showing the initial functions
and the function resulting from operations between them in
various representations (graphs, value tables, and correspondence rules).
|
|
Prepare an essay about operations between functions
|
|
Some issues to consider:
|
|
How are the oprations between functions expressed in the
different representations of the functions (value table, graph,
correspondence rule).
|
|
|
Which operations between linear functions result in a function
that is also linear? Which operations between linear functions
lead to functions that are not linear?
|
|
|
For cases in which the result of an operation between two linear
functions is a linear function, describe the relations between the properties of
the functions involved in the operation, and the properties of
the resulting function.
|
|
|
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.
|
Use the available tools to record important points for discussion and interesting or problematic cases.
|
|
|
|
