Question

Can anyone please help me with a math question about asymptotes? I know what to do.. but can you please check? -----> f(x) =x^2-25/x+4 Determine all asymptotes of this function including horizontal, vertical, and oblique (slant)
THANKS !!

Answer 1

@Megan1101 Go here

http://www.wolframalpha.com/input/?i=%28x^2-25%29%2F%28x%2B4%29+retricemptotes

Answer 2

Or.

To find the vertical asymptotes, make the denominator zero:
x + 4 = 0
x = -4
For the others, consider what happens as x approaches infinity. In that case, the -25 and +4 become insignificant as compared to the x^2 and the x, so we're left with:
f(x) = (x^2) / x = x
So the slant asymptote is y = x

Answer 3

Here is my answer: Vertical Asymptotes: x = -4
Horizontal Asymptotes: There is no horizontal Asymptotes.
But for Oblique Asymptotes: HOW DO I DIVIDE?

Answer 4

Is this the answer? http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=72d7a212d12d5f1f3d0ed5f814b8446a&title=Slant%20Asymptote%20Calculator&theme=blue&i0=x%5E2-5x%2B6&i1=x%2B4&podSelect=&includepodid=Input&includepodid=Result&includepodid=Plot&showAssumptions=1&showWarnings=1

Answer 5

I'm Not sure.

@AriPotta Can you help with some math please?

Answer 6

ok well how did you get the other answer: y = x?

Answer 7

@Megan1101 since the dividend is of the form (x-a), just use a synthetic division to get the quotient and the slant asymptote

Answer 8

umm ok well I got 2 different answers! Can you please help? @jdoe0001

Answer 9

$$
^\boxed{-4} \pmatrix{1 & 0 & -25\\
& -4 & 16\\
--& -- & --\\
1 & -4 & -9
}\\
\text{which gives me a result of } \boldsymbol{x-4}-\cfrac{9}{x+4}\\
$$
bolded non-rational part of the result is the slant asymptote

Answer 10

sorry for replying late, thank you! ;)

Answer 11

Ok I totally understand it now! thanks again!

Answer 12

yw