Question

Find the zeros, vertical asymptote, horizontal asymptote, slant asymptote, and graphing points.


`(2)/(x^2 - 4)`

Answer 1

set numerator to zero
2=0
false
no xints

VA
set denom to zero
(x-2)(x+2)=0
VA's are x=-2 and x=2

HA
p(x)/q(x)
degree of p(x)<q(x)
HA is y=0
does it cross?
0=2/(x^2-4)
0=2
false
it does not cross the HA

no slant assemtotes

a graphing point is when x=0, then y=-1/2

so what you do to graph is
draw lines
x=-2
x=2
y=0

starting from the point (0,-1/2)
draw a u shape down so you almost touch the assymtotes
then go to the left and draw a backward 'L' shape near the assemtotes
go the the right and draw an 'L' near assemtotes