Question

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

Answer 1

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]}