Asymptote Finder (Rational Function)
Vertical and horizontal asymptotes of P(x)/Q(x).
Enter your values
ⓘ Live results
Results
- Vertical asymptote
- x = 2
- Horizontal asymptote
- y = 1
- Numerator
- 1x+0
- Denominator
- 1x+-2
Quick answer
Vertical asymptotes occur where the denominator is zero (and numerator isn't); horizontal asymptote depends on the ratio of leading coefficients when degrees match.
Vertical: Q(x)=0. Horizontal: compare degrees of P and Q.
How to use the Asymptote Finder (Rational Function)
- 1Enter the numerator coefficients (set the x^2 term to 0 for a linear numerator).
- 2Enter the linear denominator's slope and intercept.
- 3The vertical asymptote is where the denominator equals zero.
Worked example
Using the values the calculator loads with:
Inputs
- Numerator: a (x^2 coeff, 0 if none)0
- Numerator: b (x coeff)1
- Numerator: c (constant)0
- Denominator slope m1
- Denominator intercept k-2
Results
- Vertical asymptotex = 2
- Horizontal asymptotey = 1
- Numerator1x+0
- Denominator1x+-2
Frequently asked questions
What about holes?
If a factor cancels between numerator and denominator, that point is a hole, not an asymptote — check for common roots.
Oblique asymptotes?
When numerator degree is exactly one more than denominator, divide to find the slant line.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.