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Calculation Machine

Asymptote Finder (Rational Function)

Vertical and horizontal asymptotes of P(x)/Q(x).

Reviewed by the Calculation Machine team · How we check our maths

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.

The formula

Vertical: Q(x)=0. Horizontal: compare degrees of P and Q.

Worked example

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

Result

  • Vertical asymptotex = 2
  • Horizontal asymptotey = 1
  • Numerator1x+0
  • Denominator1x+-2

How to use the Asymptote Finder (Rational Function)

  1. 1Enter the numerator coefficients (set the x^2 term to 0 for a linear numerator).
  2. 2Enter the linear denominator's slope and intercept.
  3. 3The vertical asymptote is where the denominator equals zero.

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