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