How do you find vertical, horizontal and oblique asymptotes for f(x)=(5x^2-x+3)/(x+3)?

Apr 13, 2016

Vertical asymptote is $x = - 3$
No horizontal asymptote
Oblique asymptotes is $y = 5 x - 16$

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.

Given below is the step-by-step walk through

The curve will never touch the line $x = - 3$, thereby making it the vertical asymptote.

Next, we find the horizontal asymptote:
Compare the degree of the expressions in the numerator and the denominator.
Since the degree in the numerator is greater than the degree in the denominator, there are no horizontal asymptote.

The oblique asymptote is a line of the form y = mx + c.
Oblique asymtote exists when the degree of numerator = degree of denominator + 1

To find the oblique asymptote divide the numerator by the denominator.

The quotient is the oblique asymptote.
Therefore, the oblique asymptote for the given function is $y = 5 x - 16$.