# Thread: How to find oblique Asymptote

1. ## How to find oblique Asymptote

How do you find the oblique asymptote of 2X^2/ X-4

2. Originally Posted by supersaiyan
How do you find the oblique asymptote of 2X^2/ X-4
To find oblique (or "slant") asymptotes, do the polynomial long division:

[html] 2x + 8
----------------
x - 4 ) 2x^2 + 0x + 0
2x^2 - 8x
----------------
8x + 0
8x - 32
----------------
32[/html]
So the slant asymptote will be y = 2x + 8.

3. Thanks, that what I thought but my teacher said it's just 2X

4. Originally Posted by supersaiyan
Thanks, that what I thought but my teacher said it's just 2X
Graph the function and look. Does the slant asymptote appear to pass through the origin, or not? (Make sure you "zoom out" on the graph, so you can see what's going on off to the sides. The slanty trend of the curve does not correspond to a line through the origin!)

5. Originally Posted by supersaiyan
Thanks, that what I thought but my teacher said it's just 2X
If the equation is $y = \frac{2x^2}{x} - 4$ then your teacher is correct.

If the equation is $y = \frac{2x^2}{x - 4}$ then your teacher is wrong.