28Asymptotes of a rational function

Find the vertical and horizontal asymptotes of $\displaystyle f(x) = \dfrac{3x - 1}{x + 4}$.

The graph has a vertical asymptote at x = −4, where the denominator (x+4) hits zero, and a horizontal asymptote at y = 3, from the ratio of leading coefficients 3/1 since top and bottom degrees match. Checking with x = 1000 gives f(x) ≈ 2.99, close to 3.