Limits and Continuity — Continuity

About this lesson

This unit covers the concept of continuity of a function at a point and on an interval. It begins by using graphs to illustrate continuous and discontinuous curves, then formalizes the definition of continuity at a point: the limit exists, the function is defined at the point, and the limit equals the function value. The unit provides worked examples of discussing continuity at specific points, including piecewise functions, and shows how to redefine a function to make it continuous at a point when possible. It also discusses continuity on an interval, stating conditions for a function to be continuous on a closed interval, and lists types of functions that are continuous on their domains (polynomial, rational, sine, cosine, tangent). The text includes many exercises for students to practice discussing continuity at points and on intervals, and to find values of constants that make functions continuous.