# How do you find vertical, horizontal and oblique asymptotes for y =(3/x)+2?

Feb 22, 2017

Vertical asymptote: $x = 0$
Horizontal asymptote: $y = 2$
Oblique asymptote: none

#### Explanation:

Find a common denominator for the function:
$y = \frac{3}{x} + \frac{2 x}{x} = \frac{3 + 2 x}{x} = \frac{2 x + 3}{x}$

Rational Function: $\frac{N \left(x\right)}{D \left(x\right)}$, when $N \left(x\right) = 0$ gives x-intercepts,
when $D \left(x\right) = 0$ you find vertical asymptotes.

Vertical asymptote at $x = 0$

When $\frac{N \left(x\right)}{D \left(x\right)} = \frac{{a}_{n} {x}^{n} + \ldots .}{{b}_{m} {x}^{m} + \ldots .}$ where $n , m$ are the degrees of the polynomials.

If $n = m$ horizontal asymptote is at $y = {a}_{n} / {b}_{m}$

$n = m = 1$, so Horizontal asymptote: y = 2/1; y = 2

To have an oblique or slant asymptote, $m + 1 = n$ which is not the case, so there is no oblique asymptote.