# How to find the asymptotes of f(x)=2 - 3/x^2?

Apr 22, 2016

Vertical asymptote is $x = 0$ or $y$-axis

Horizontal asymptote is $y = 2$

No oblique asymptote.

#### Explanation:

An ASYMPTOTE is a line that approches a curve, but NEVER meets it.

To find the vertical asymptote , put the denominator = 0 (because 0 cannot divide any number) and solve. This is where the function cannot exist.

Given below is the step-by-step walk through:

The curve can never touch $x = 0$, or the $y$-axis , thus making it the vertical asymptote.

To find the horizontal asymptote , compare the degree of the expressions in the numerator and the denominator.

First, lets re-write the expression so we have one a common denominator.

Now we can compare the degrees of the numerator and the denominaotr.

The degree of the numerator = 2 and the degree of the denominator = 2.
Since the degrees are equal, the horizontal asymptote

$y = \left(\text{numerator's leading coefficient"/"denominator's leading coefficient}\right)$

$y = \frac{2}{1} \implies y = 2$

The oblique asymptote is a line of the form y = mx + c.
Oblique asymptote exists when the degree of numerator = degree of denominator + 1
Here, the degree of the numerator = degree of the denominator = 2.
Therefore, the given function has no oblique asymptotes.