Discontinuities
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A discontinuity of a function at a point where the function has finite, but unequal, limits as the independent variable approaches the point from the left and from the right.
Removable
A point on the graph that is undefined or does not fit the rest of the graph.
Infinite
Exists when one of the one-sided limits of the function is infinite. If the two one-sided limits have the same value, then the two-sided limit will also exist.
Continuous
a function for which small changes in the input result in small changes in the output.