# How do you find the asymptotes for y = 3/(x + 4)?

Aug 16, 2016

vertical asymptote at x = - 4
horizontal asymptote at y = 0

#### Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: $x + 4 = 0 \Rightarrow x = - 4 \text{ is the asymptote}$

Horizontal asymptotes occur as

${\lim}_{x \to \pm \infty} , y \to c \text{ (a constant)}$

divide terms on numerator/denominator by x

$\frac{\frac{3}{x}}{\frac{x}{x} + \frac{4}{x}} = \frac{\frac{3}{x}}{1 + \frac{4}{x}}$

as $x \to \pm \infty , y \to \frac{0}{1 + 0}$

$\Rightarrow y = 0 \text{ is the asymptote}$
graph{(3)/(x+4) [-10, 10, -5, 5]}