Jessica --

You can get information about any function in Mathematica from the Documentation center, under the Help menu (at least on my Mac). Once there, you can type in Abs, and get a lot of information. (The same functionality is present on the wolfram website in the Suport menu on the main Wolfram page.

Basically, Abs gives the absolute value of real or complex z. It is left unevaluated if z is not numeric.

You should make the documentation center your friend. Since version 6, it has replaced the printed Mathematica book. You will find information about functions, tutorials and guides.

Also under the Help menu is an item for the virtual book. This is a direct, electronic replacement for the printed book. You should probably read through topics that interest you. The neat thing about this (and the documentation center in general) is that there are 'live' computations. You can alter the examples given in the text and see what happens. You can also cut and paste code into your own notebooks.

As an example, you could read about Manipulate[] in the documentation, and then use the code that Sean provided to zoom in on points close to {0,0} by making the plot limits into a dynamic variable manipulated with a slider.

Manipulate[

Plot[{Abs[x], -Abs[x], x Sin[1/x]}, {x, -lim, lim},

PlotStyle -> {Red, Blue, Green}], {{lim, .3}, 0.000000000001, .5}]