# How do you find the asymptotes for  f(x)= (x+5)/(x+3)?

Feb 20, 2016

vertical asymptote at x = -3
horizontal asymptote at y = 1

#### Explanation:

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

solve x + 3 = 0 $\Rightarrow x = - 3$

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

If the degree of the numerator and denominator are equal , the equation can be found by taking the ratio of leading coefficients. Here they are both degree 1.

$\Rightarrow y = \frac{1}{1} = 1 \text{ is the equation}$

Here is the graph of the function as an illustration.
graph{(x+5)/(x+3) [-10, 10, -5, 5]}