Asymptote Finder (Rational Function)
Vertical and horizontal asymptotes of P(x)/Q(x).
Enter your values
Enter the numerator: a (x^2 coeff, 0 if none) you are working with.
Enter the numerator: b (x coeff) you are working with.
Enter the numerator: c (constant) you are working with.
Enter the denominator slope m you are working with.
Enter the denominator intercept k you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
At a glance
| What it does | Vertical and horizontal asymptotes of P(x)/Q(x). |
|---|---|
| Category | Math |
| Inputs needed | Numerator: a (x^2 coeff, 0 if none), Numerator: b (x coeff), Numerator: c (constant), Denominator slope m, Denominator intercept k |
| Main output | Vertical asymptote |
| Formula | Vertical: Q(x)=0. Horizontal: compare degrees of P and Q. |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Numerator: a (x^2 coeff, 0 if none)
- Enter the numerator: a (x^2 coeff, 0 if none) you are working with.
- Numerator: b (x coeff)
- Enter the numerator: b (x coeff) you are working with.
- Numerator: c (constant)
- Enter the numerator: c (constant) you are working with.
- Denominator slope m
- Enter the denominator slope m you are working with.
- Denominator intercept k
- Enter the denominator intercept k you are working with.
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.
What do I need to enter into the Asymptote Finder (Rational Function)?
Just 5 values: numerator: a (x^2 coeff, 0 if none), numerator: b (x coeff), numerator: c (constant), denominator slope m, denominator intercept k. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Asymptote Finder (Rational Function) work out the 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. It applies the formula Vertical: Q(x)=0. Horizontal: compare degrees of P and Q. and shows the working so you can check each step by hand.
Is the Asymptote Finder (Rational Function) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.