This gives practice for finding and classifying discontinuities of rational functions.

How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Theoretically Easier Difficulty Problem

To determine if a rational function is continuous at a specific x-value, try computing the function at that x-value.
If the denominator is zero at that value, then the function is continuous. If you can compute at the given x-value and get a finite (well defined) number, then it is continuous.

Consider the function: At the -value the function :

1:
is continuous
2:
is not continuous

Theoretically Medium Difficulty Problem

To determine if a rational function is continuous at a specific x-value, try computing the function at that x-value.
If the denominator is zero at that value, then the function is continuous. If you can compute at the given x-value and get a finite (well defined) number, then it is continuous.

Consider the function: At the -value the function :

1:
is continuous
2:
has a hole discontinuity
3:
has a vertical asymptote discontinuity

Theoretically Harder Difficulty Problem

To determine if a rational function is continuous at a specific x-value, try computing the function at that x-value.
If the denominator is zero at that value, then the function is continuous. If you can compute at the given x-value and get a finite (well defined) number, then it is continuous.

Consider the function: At the -value the function :

1:
is continuous
2:
has a hole discontinuity
3:
has a vertical asymptote discontinuity