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

Mar 9, 2016

vertical asymptote x = -2
horizontal asymptote $y = \frac{5}{2}$

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve: 2x + 4 = 0 → x = - 2 is the asymptote

Horizontal asymptotes occur as lim_(x→±∞) f(x) → 0

If the degree of the numerator and denominator are equal, as in this case , both of degree 1 . the equation can be found by taking the ratio of leading coefficients.

$\Rightarrow y = \frac{5}{2} \text{ is the asymptote }$

Here is the graph of the function.
graph{(5x-15)/(2x+4) [-20, 20, -10, 10]}