Question

find vertical asymptotes horizontal asymptotes y int and x int of rational function:

R(x) = (1-3x^2)/(x^2+4x-12)

Answer 1

To find the vertical asymptotes you need to look at where the denominator is zero, so factor it. Then for the horizontal asymptote take the ratio of the leading powers. In this case:
\[-3x^2/x^2 \]
because this will tell you the long term behavior (when x gets really large or really small).

Answer 2

soooo what does thtat mean?

Answer 3

so -3 is my vertical asymptote?

Answer 4

Well x^2+4x-12 = (x+6)(x-2)...So your asymptotes are where that is zero which occur at... (fill in here)?

And the horizontal asymptote is the ratio that I gave you... think about it.

Answer 5

-6 and 2?

Answer 6

those are vertical asymptotes right?

Answer 7

Yup.

Answer 8

ok I got that right now hwat about the horizontal ones?

Answer 9

Well there is only one and its the ratio that I gave you -3x^2/x^2. If the leading power in the denominator is bigger then the asymptote is at zero, if its smaller there is no asymptote, and if they are the same power it is the ratio giving us -3.

Answer 10

okay thanks, and if I wanted to find the intercepts on the graph I could just graph it right?