How to Find Vertical Asymptote of a Rational Equation - Definition, Example

How to Find Vertical Asymptote of a Rational Equation - Tutorial

Definition:

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.

How to determine the vertical Asymptote?

Method 1:

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

Vertical Asymptotes

Method 2:

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

Example:

Find the vertical asymptotes of equation


Vertical Asymptotes Function

Method 1:

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.


Vertical Asymptotes Function

is a large positive number. Intuitively, we see that Vertical Asymptotes

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.

Vertical Asymptotes
Vertical Asymptotes

The line x = 3 is the vertical asymptote.

Method 2:

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

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