Helping Grandaughter with her Algerbra 2.

Been awhile since I've done this stuff

Hopefully some kind soul will _carefully_ check & correct me on the following...

Given a Rational Function Fx = Px/Qx

1 - When Qx = 0 you have a "discontinuity" (Because you can't divide by zero)

2 - To find the points of discontinuity she simply sets the denominator equal to zero and solves for the variable.

3 - You also have a vertical asymptote at these points UNLESS the numerator is also equal to zero.

4 - If both the numberator and the demoniator equal zero at the same time... for the same value of X... you have a "hole" ... .right?

5 - The point at which the "hole" occurs is actually a point of discontinuity as well... but there is no vertical asymptote... just a break in the graph... right?

Thanks for any help.