MA 141 Study Guide - Final Guide: Function Composition, Intermediate Value Theorem
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We now have the tools to formally de ne a continuous function. Def: a function f is continuous at the point x0 if: f is de ned at x0, so f (x0) exists, lim f (x) exists. x x0, lim f (x) = f (x0). x x0. If a function is continuous at every point x0 in its domain, we say it is continuous on its domain. This reinforces why we called the "weird" graphs in section 1. 1 discontinuities. In the rst picture, lim f (x) does not exist, since the function is approaching two di erent x x0 values from the left and the right. In the second picture, both the function value and the limit exist at x0, but they are not equal. 3x2 x + 2 x4 2x2 + 1 is continuous on its domain. First, let"s nd the domain of f (x).
