Introduction: The more one studies mathematics, the more one encounters the concept of a function. By talking about functions we come to understand how they encode information. To bring a deeper understanding to functions we give them visual expression. Seeing the information of a function presented in a variety of forms helps us recognize more concretely some of its fundamental features.
These resource materials have been developed to help students understand functions more sensibly and deeply using four common ways to present the encoded information of a function. Students may have encountered some of these methods previously, but in this resource you will see how each of these methods give us different ways to view the same underlying relation.
The four ways that connect an understanding of functions are:
Tables of data for "variable" quantities.
Algebraic equations that determine a method for determining the value of (controlled or dependent) variable quantities uniquely from the value of other (controlling or independent) variable quantities.
The visualization of data for variable quantities using the Cartesian coordinate system.
The visualization of data for variable quantities [b]using mapping diagrams.[/b]
For more textual connections see: [url]http://users.humboldt.edu/flashman/MD/section-1.1VF.html[/url]
