**
Continuity
** -
A function is continuous at a point if the three following conditions are met:
1)

*f* (*a*) is defined. 2)

*f* (*x*) exists. 3)

*f* (*x*) = *f* (*a*). A conceptual way to describe continuity is this: A function is
continuous if its graph can be traced with a pen without lifting the pen from
the page.

**
Infinite Discontinuity
** -
A category of discontinuity in which a vertical
asymptote exists at *x* = *a* and *f* (*a*) is
undefined.

**
Jump Discontinuity
** -
A category of discontinuity in which

*f* (*x*)≠*f* (*x*), but both of these limits exist and are finite.

**
Limit
** -
The value *A* to which a function *f* (*x*) gets arbitrarily close as the value of
the independent variable *x* gets arbitrarily close to a given value *a*. Such
a limit is symbolized this way: *lim*_{xâÜ’a}*f* (*x*) = *A*.

**
One-Sided Limit
** -
A limit based entirely on the values of a function taken at an

*x*-value
slightly greater than or less than a given value. Whereas a two-sided limit

*f* (*x*) takes into account the values of

*x* near

*a* which are
both greater than and less than

*a*, a one-sided limit from the left

*f* (*x*) or from the right

*f* (*x*) takes into account only
values of

*x* less than

*a*, or greater than

*a*, respectively.

**
Point Discontinuity
** -
A category of discontinuity in which a function has a well-defined two-sided
limit at *x* = *a*, but either *f* (*x*) is not defined at *a* or its value at
*a* is not equal to this limit.