Question

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

Answer 1

This function has a horizontal asymptote at `y=5/2` and a vertical asymptote at `x=-2`.

Explanation:

`f(x)=(5x-15)/(2x+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=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`.