Question

Determine the vertical asymptote for the rational function f(x) = x - 4 over 2x + 3.

Answer 1

Vertical asymptotes happen at x=a if the function is undefined at x=a.

This is a rational functions, and rational functions are not defined when the denominator is zero, since you can't divide by zero.

In this case, the denominator is zero if

$2x+3=0 \iff 2x=-3 \iff x=-\drac{3}{2}$

And thus the function has a vertical asymptote at x= -3/2