Math Rational Functions
posted by Mae on .
1. Some rational functions have asymptotes, others have holes, and some have both. Explain how you can identify, without graphing, which graphical features a rational function will have.
Can someone explain this thoroughly ? I don't understand. thanks in advance.

the culprit for asymptotes and holes is the denominator.
If for some value of the variable, then denominator is zero, but the numerator is NOT zero, you will have an asymptote.
If for some value of the variable, then denominator is zero, but the numerator is ALSO zero, you will have a hole
e.g. y = (x2)/(x^2  4)
notice this reduces to y = 1/(x+2)
so if x = 2 in the original we get 0/0, so there is a hole at (2,1/4)
if x = 2 we get 4/0 in the original, so x = 2 is an asymptote 
how would we know if it has both holes and asymptotes?

What is the domain and range of 2x^218/x^2+3x10