# How to find the asymptotes of R(x)=(4x)/(x-3)?

Feb 4, 2016

vertical asymptote at x = 3
horizontal asymptote at y = 4

#### Explanation:

A vertical asymptote will occur as the denominator of a rational function tends to zero. To find the equation let denominator equal zero.

solve : x - 3 = 0 $\Rightarrow x = 3 \textcolor{b l a c k}{\text{ is the equation}}$

[ A horizontal asymptote will occur as  lim_(x→±∞) f(x) →0 ]

If the numerator and denominator of a rational function are of equal degree the then equation of the asymptote can be found by taking the ratio of leading coefficients.

Here they are of equal degree , both of degree 1 .

equation is $y = \frac{4}{1} = 4$

Here is the graph of the function as an illustration.
graph{4x/(x-3) [-40, 40, -20, 20]}