Continuity

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Reminders

Condition 1: f(c) exists

Condition 2: the limit of x as it approaches c f(x) exists

Condition 3: the limit of x as it approaches c f(x) = f(c)

A jump discontinuity occurs when the curve "breaks" at a particular place and starts somewhere else. In other words, lim x-> a^- f(x) is not equal to lim x->a^+ f(x)

A point discontinuity occurs when the curve has a "hole" in it from a missing point because the function has a value at that point that is "off the curve." In other words, lim x->a f(x) is not equal to f(a)

An essential discontinuity occurs when the curve has a vertical asymptote.

A removable discontinuity occurs when you have a rational expression with common factors in the numerator and denominator. Because these factors can be canceled, the discontinuity is "removable".