How to find the asymptotes of #f(x)=2 - 3/x^2#?
Vertical asymptote is
Horizontal asymptote is
No oblique asymptote.
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
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
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.