Section Summary: 1.1

  1. Definitions

  2. Theorems

    There are no explicit theorems in this chapter, although the vertical line test is really a sort of theorem: it tells us that a graph without multiple intersections with any vertical line represents a function (and that a graph with two intersections with a vertical line is not a function).

  3. Properties/Tricks/Hints/Etc.

    There are (at least) four representations of a function:

    Convention: If a function is given by a formula and the domain is not stated explicitly, the convention is that the domain is the set of all numbers for which the formula makes sense. (thanks Tosin!

  4. Summary

    This section reviews the definition and properties of functions, and presents four ways to represent them (noted above). Properties studied include symmetry, monotonic behavior (increasing or decreasing), and the piece-wise definition of a functions. Some attention is paid to the vertical line test for whether a graph represents a function y=f(x), and to modeling real-life data with formulas.





LONG ANDREW E
Tue Jan 9 22:42:05 EST 2001