## onegirl Group Title Determine all horizontal, slant, and vertical asymptotes. For each vertical asymptote, determine whether f(x) -> infinity sign of f(x) -> negative infinity sign on either side of the asymptote. one year ago one year ago

1. onegirl Group Title

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

2. satellite73 Group Title

is it $\frac{x^2}{4-x^2}$?

3. onegirl Group Title

yes

4. satellite73 Group Title

ok so for the vertical asymptotes, set the denominator equal to zero and solve for $$x$$

5. onegirl Group Title

ok

6. satellite73 Group Title

you get $4-x^2=0$ or $(2-x)(2+x)=0$ and the solutions are $$x=-2$$ or $$x=2$$ those are your vertical asymptotes (there are two of them)

7. onegirl Group Title

ok

8. satellite73 Group Title

for the horizontal asymptote, note that the numerator and denominator have the same degree (both are degree 2) so it is the ratio of the leading coefficients

9. onegirl Group Title

okay

10. satellite73 Group Title

the leading coefficient of $$x^2$$ is 1 and the leading coefficient of $$4-x^2$$ is $$-1$$ therefore the horizontal asymptote is $$y=-1$$

11. satellite73 Group Title

that is in the case where the degrees are the same. there is no slant asymptote for there to be a slant asymptote , the degree of the numerator would have to be one more than the degree of the denominator

12. onegirl Group Title

okay thx

13. satellite73 Group Title

yw