Asymptote Calculator

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Asymptote is a line which is drawn to a curve heading towards infinity, and the distance between the line and the curve approaches ‘0’, however the asymptote never touches or crosses the curve. Asymptote calculator is a great tool useful in finding the vertical or horizontal asymptote for any given function.

Example 1: Find the vertical and horizontal asymptotes to the function:

y = (3x2 + 5) / (x2 – 3x +2)

To find the vertical asymptote, set the denominator = 0.

x2–3x + 2 = 0

(x–2)(x-1) = 0   x–2=0 (or) x–1=0

The vertical asymptotes are x = 2 and x = 1

Highest exponent of ‘x’ in numerator = Highest exponent of ‘x’ in denominator

Horizontal asymptote,  Divide the leading terms, 3x2 and x2 by ‘x2’ = 3/1 = 3

Horizontal asymptote  y = 3

Example 2: Find the vertical and horizontal asymptotes to the function:

y = (x – 4) / (x2 – 9)

To find the vertical asymptote, set the denominator = 0.

x2 – 9 = 0   (x-3)(x-3) = 0

The vertical asymptote is x = 3

Highest exponent of ‘x’ in numerator

In this case, the function or the curve towards infinity will get closer and closer to the X-axis.

Hence in this case, always the horizontal asymptote  y = 0