Find the vertical and horizontal asymptotes of f(x) = (2x + 3)/(x - 4).

Step 1: Find the vertical asymptote.

A vertical asymptote of a rational function can occur where the denominator equals zero, provided the factor does not cancel with the numerator.

Set the denominator equal to zero:
x - 4 = 0

Solve:
x = 4

The numerator at x = 4 is:
2(4) + 3 = 11

Since the numerator is not zero, the factor does not cancel. Therefore, x = 4 is a vertical asymptote.

Step 2: Compare the degrees to find the horizontal asymptote.

The numerator 2x + 3 has degree 1.
The denominator x - 4 also has degree 1.

When the numerator and denominator have the same degree, the horizontal asymptote is the ratio of their leading coefficients.

Step 3: Find the ratio of the leading coefficients.

The leading coefficient of the numerator is 2.
The leading coefficient of the denominator is 1.

Therefore:
y = 2/1 = 2

So the horizontal asymptote is y = 2.

Therefore, the vertical asymptote is x = 4 and the horizontal asymptote is y = 2.