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