Question

How do I get the asymptote to a question like R(x) = 3x/(x+4)

Answer 1

You have the following function;

$R(x)=\frac{3x}{x+4}$

the vertical asymptote is obtained by making the denominator equal to zero and solving for x:

x + 4 = 0

x = -4

The vertical asymptote is x = -4

The horizontal asymptote, for the cases in which the degree of the numerator is equal to the degree of the denominator, is equal to the quotient between the leadding coefficients:

y = 3/1 = 3

The horizontal asymptote is y = 3