Point of Discontinuity
A point of discontinuity of a is a point where the -coordinate makes the function value . Often, this occurs when the coordinate makes the denominator equal to Below is an example.
is not in the of the function
it is a point of discontinuity. There is no way to rewrite the expression so that
becomes a valid input. Therefore, it is called a non-removable point of discontinuity
. Below is another example.
In the function above,
is a point of discontinuity because when
the denominator is equal to
However, the expression can be simplified using the .
After simplifying, the value
is now a valid input. Therefore, it is called a removable point of discontinuity
A removable discontinuity, like the one at is typically called a
hole in the graph.