Saturday, January 28, 2017

Introduction to the notion of continuity of functions

In general, something that is continuous continues without interruption. If during a jogging you run from point A to B without stopping your running is continuous. However, if you stop even once the running is discontinuous. A line of cars in traffic that never stop is continuous. If the cars stop the line is discontinuous. If you draw a straight line without lifting your pencil the line is continuous. If you draw a straight line with dots you lift your pencil several times. The line is discontinuous at every dot.

The graph of the linear, parabolic, third-degree functions is an unbroken curve. It can be drawn without lifting the pencil from the paper. In general, the polynomial functions are continuous because their limit exists everywhere in the domain of the real numbers. A function of which the graph has holes, jumps or breaks is not continuous. Such functions are discontinuous.You have to lift your pencil to draw their graph.

Watch these videos to get an idea of what it means for a function to be continuous.

Interested about an Introduction to Calculus course take this one for free Introduction to Calculus or if you prefer take the complete Calculus course Calculus AB