Continuity of Functions Introduction
Daisy, track extraordinaire, is hiking the Appalachian Trail in central Pennsylvania. It's her dream to hike the entire trail from Georgia to Maine. It's been raining ever since she crossed the Mason-Dixon line, but that's not enough to make her quit. She hikes on, until she reaches a stream. The stream is far deeper than usual, and is way too dangerous to ford. There's a discontinuity in the trail so to speak. She doesn't have time to wait for the water to recede, and she's come too far to turn back. Daisy can handle any discontinuities this trail throws her way, though. She looks around for a sturdy tree limb and fashions a 14-foot pole. She uses it to successfully leap across the stream, and continues on her way. Boom. Pole vaulted.
We can also talk about the continuity or discontinuity of functions. If a function contains breaks, that function isn't continuous.
In this chapter we'll use graphs and formulas to describe continuity. Understanding continuity will also give us some freebie information about functions, and who doesn't like free stuff?