Rational Function Asymptotes

Build a rational function by toggling factors. Denominator-only roots give vertical asymptotes; a root in both gives a hole; the degrees decide the end behavior.

f(x) =

Numerator factors (x − r):

Denominator factors (x − r):

leading a 1

Try: put x = 1 in BOTH numerator and denominator — the vertical asymptote becomes a hole (open circle), because the factor cancels.