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A CLASSROOM NOTE: BAR CODE SCANNER AS A CANONICAL FUNCTION

PROPERTIES OF FUNCTIONS

In precalculus several properties of functions of a single variable need to be presented and understood early in the course if students are going to understand the abstract parts of precalculus.

* The independent and dependent variable

It is particularly tricky to distinguish between these two variables since many elementary functions are invertible. While there are interesting problems that involve reversing the relationship between these two variables, when functions are first introduced it is probably better to use examples that have a clear independent and dependent variable.

* Formulas

Some functions like f(x) = x + 5 are computed using a formula (adding 5 to ...

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