Question

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

Answer 1

Zeroes
set numerator to zero
x^2=0
x=0
zeroes are at (0,0)

HA

for p(x)/q(x)

when degree of p(x)<q(x), HA=0

when degree of p(x)=q(x), HA= leading coef of p(x) divided by leading coef of q(x)

when degree of p(x)>q(x) you probably have a slant assymtote

degrees are same (no slant assymtote)

leading coefs

1/1=1

HA is y=1

does it cross?

1=(x^2)/(x^2-4)

x^2-4=x^2

minus x^2 both sides

-4=0

false, it does not cross the HA

VA

simplify the fraction (it can't)

set the denomenator to zero

(x-2)(x+2)=0

VA's at x=2 and x=-2

so to graph

graph the point (0,0)

draw the lines

y=1

x=-2

x=2

reemmber, plus, minus, plus

so from left, it goes from above the HA right up to the VA of x=-2

then goes upside down U shape in between VA's going through (0,0)

then from top of VA x=2 down to y=1 then gets closer to y=1 but never touches