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

1 Answer
Feb 4, 2016

Answer:

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]}