# How do you find the vertical, horizontal or slant asymptotes for (4x)/(x-3) ?

Feb 29, 2016

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

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation equate the denominator to zero.

solve : x - 3 = 0 → x = 3 is the equation

Horizontal asymptotes occur as lim_(x →±∞) f(x) → 0

If the degree of the numerator and denominator are equal, as they are here , both of degree 1 , then the equation can be found by taking the ratio of leading coefficients.

$y = \frac{4}{1} = 4 \Rightarrow y = 4 \text{ is the equation }$