Question

Help with graphing, will give a medal!

(problem below)

Answer 1

\[\frac{ x^3-1 }{ x^2-4 }\]

Answer 2

it might help to rewrite it as
\[y=\frac{(x-1)(x^2+x+1)}{(x+2)(x-2)}\]

Answer 3

that way you see that there are vertical asymptotes at \(x=-2\) and at \(x=2\)

Answer 4

I already reached those steps, but I'm having alot of trouble graphing this equation because of the slant asymptote

Answer 5

it might also be useful to divide since the numerator is degree one more than the denominator
you will get \(y=x+fractions\)

Answer 6

that means the slant asymptote is the line \(y=x\)

Answer 7

did you get y=x from long division?

Answer 8

yes, except i didn't really do it
just eyeballed it

Answer 9

\(x^3\) divided by \(x^2\) is \(x\) and the rest is the remainder, which will go to zero as \(x\) goes to infinity
but you can do the long division too, just ignore the remainder

Answer 10

ahh, ok. Just curious, can asymptotes ever be passed?

Answer 11

vertical no

Answer 12

horizontal yes

Answer 13

ok, cool, I think I got it from here, thanks for your help!

Answer 14

yw
test a few points and you will see what it looks like
has to respect those asymptotes

Answer 15

ok thank you again :)