Continuous functions are continuous at all of the points in their domains. In essence, these are functions whose graphs can be drawn with a single brush stroke.
Review your understanding of continuity with some challenge problems.
The intermediate value theorem states that if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval. This is a basic but important property of all continuous functions.
A function is continuous at a point if its limit at that point exists and is equal to the actual function's value at that point.
Limits_of_combined_composite_functions
Practice your basic understanding of limits and continuity with more complex cases.
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