An asymptote is a line that a graph approaches, but does not intersect. Horizontal asymptote of rational equation can be found when the highest degree of polynomial is equal in both the numerator and denominator.

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)

If the polynomial degree of x in the numerator is equal to the polynomial degree of x in the denominator , then y = c. Value of c can be obtained by dividing the leading coefficients.

If the polynomial degree of x in the numerator is less than the polynomial degree of x in the denominator then y = 0. This is called as horizontal asymptote.

Find the horizontal asymptotes of the following function.

Divide both numerator and denominator by x.

The line ** y = 2/ 3 **is the **horizontal asymptote**.

The polynomial degree of x in the numerator is equal to the polynomial degree of x in the denominator.

Then dividing the leading coefficients we get 2/3.

The line ** y = 2/ 3 **is the horizontal asymptote.

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