# How do you find the Vertical, Horizontal, and Oblique Asymptote given f(x)= (3x + 5) /( x - 2)?

Nov 11, 2016

The vertical asymptote is $x = 2$
There is no oblique asymptote.
The horizontal asymptoteis $y = 3$

#### Explanation:

As you cannot divide by $0$, the vertical asymptote is $x = 2$

The degree of the numerator is $=$ to the degree of the denominator, there is no oblique asymptote.

${\lim}_{x \to \pm \infty} f \left(x\right) = 3 \frac{x}{x} = 3$

Therefore $y = 3$ is a horizontal asymptote
graph{(y-(3x+5)/(x-2))(y-3)=0 [-25.65, 25.65, -12.83, 12.84]}