Question

How do I find the horizontal and vertical asymptotes of f(x)= 2/x^2-2x-3?

Also would like to check if my x and y intercepts are correct.

Answer 1

I love doing this

for a function p(x)/q(x)
if degree of p(x)<q(x), the horizontal assemtote is y=0
if degrees are equal, divide linear coefients

horzontal assemtotes
first simplify
then set denom to zero and solve for x values


so

f(x)=2/(x^2-2x-3)
less so HA=y=0
doesn't cross HA

VA, set denom to zer
x^2-2x-3=0
(x-2)(x-1)=0
HA, at x=1 and x=2

xint, set y=0 and solve
not applicatble, no xint
yint, set x=0
ying=-2/3



HA is y=2, doesn't cross it
VA's at x=1 and x=2
no xint
yint at (0,-2/3)