An asymptote is a line that a graph approaches, but does not intersect. In this lesson, we will learn how to find vertical asymptotes, horizontal asymptotes and oblique (slant) asymptotes of rational functions.

When the line y = L , then its called as horizontal asymptote of the curve y = f(x) if either

For the rational function, f(x) y= 0 is the vertical asymptote when the polynomial degree of x in the numerator is less than the polynomial degree of x in the denominator. If the polynomial degree of x is same in the numerator and denominator then y = c, where c is obtained by dividing the leading coefficients

Find the vertical asymptotes of equation

Here though x is larger its close to 3, 2x is close to 8 and the value of the denominator x – 3 is the small positive integer.

is a large positive number. Intuitively, we see that

Likewise, if x is smaller and close to 3, 2x is close to 8 and the value of the denominator x – 3 is the small negative value. Below shown f(x) is a large negative number.

The line x = 3 is the vertical asymptote.

f(x) is in reduced form. X – 3 is the denominator, so the Vertical Asymptote is at x = 3.

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