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

##### 1 Answer

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

# rArr x = 3 color(black)(" 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 = 4/1 = 4 # Here is the graph of the function as an illustration.

graph{4x/(x-3) [-40, 40, -20, 20]}