What is the Oblique Asymptote?

Question

What is the Oblique Asymptote?
Can you also gimme an example?

Thanks :)

Answer 1

A rational function will have an oblique asymptote if the power of the numerator exceeds the power of the denominator (by 1 , for a straight line asymptote)
eg y =(x^2 -3x) / (x+1)

the asymptote will be the line y=x-4
this is found by dividing the denominator into the numerator

Answer 2

There are three types of asympotes--vertical, horizontal and oblique (or slant). A slant asymptote is on an angle and can occur when the numerator has a greater power of x, than the denominator.

y = (3x² + 4) / (x - 2)

If you do the division you get:

y = 3x + 6 + 16/(x - 12)

As x→∞ The equation approaches that of a line y = 3x + 6 as the value of the remaining fraction approaches zero. The slant asymptote then is:

y = 3x + 6

Here is a link.

http://www.purplemath.com/modules/asymtote3.htm

Answer 3

oblique asymptatote is the asymptote lying along the line found by log dividing the numerator of a rational fxn by the denominator of the fxn. It only occurs when power of denominator is 1 less than the numerator


f(x)= (x^2+5x+6)/(x+4)

long divide x+4 into x^2+5x+6 and youll get x+1 as a quotient and a remainder of 2 so the oblique asyptote is the line x+1 the graph approaches the line x+1