Vertical and horizontal asymptotes and ROC

Is the function discontinuous or continous. If discontinuous what type of discontinuity?

Removeable discontinuity, there is a hole which can be factored out

Is the function discontinuous or continous. If discontinuous what type of discontinuity?

Non-removable discontinuity, there is a vertical asymptote

For a horizontal asymptote, if the function’s numerator>denominator, the limit equals

infinity

For a horizontal asymptote, if the function’s denominator>numerator, the limit equals

0

For a horizontal asymptote, if the function’s denominator=numerator, the limit equals

the numerator’s coefficient of the leading power over the denominator’s coefficient of the leading power