Question

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

Answer 1

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 = 4/1 = 4 rArr y = 4 " is the equation "`