# How do you find the asymptotes for f(x)=(5x-15)/(2x+4)?

This function has a horizontal asymptote at $y = \frac{5}{2}$ and a vertical asymptote at $x = - 2$.
$f \left(x\right) = \frac{5 x - 15}{2 x + 4}$ is a rational function where the degree of the numerator and denominator are equal (they're both equal to 1).
Therefore, it has a horizontal asymptote at the value of $y$ that is the ratio of the coefficients of the leading terms (highest powers of $x$), which is $y = \frac{5}{2}$.
Since the denominator is zero when $x = - 2$ and the numerator is not zero there, it also has a vertical asymptote at $x = - 2$.