Finding horizontal asymptotes with a square root in the denominator

[CallMeShady]

Homework Statement

Homework Equations

None

The Attempt at a Solution

I was able to find a vertical asymptote at x=-3/8 by setting the denominator to 0 and using the quadratic formula to find the roots. However, I am unsure of how to find the horizontal asymptotes, and I am not 100% confident that my vertical asymptote is correct. The confusion that I have here is with the square root in the denominator.

 

[SammyS]

Homework Statement

Homework Equations

None

The Attempt at a Solution

I was able to find a vertical asymptote at x=-3/8 by setting the denominator to 0 and using the quadratic formula to find the roots. However, I am unsure of how to find the horizontal asymptotes, and I am not 100% confident that my vertical asymptote is correct. The confusion that I have here is with the square root in the denominator.

Recheck that result you get from "setting the denominator to 0 and using the quadratic formula to find the roots".

For the horizontal asymptote(s), find the limit of your function as x → ± ∞ .

 

[CallMeShady]

Recheck that result you get from "setting the denominator to 0 and using the quadratic formula to find the roots".

For the horizontal asymptote(s), find the limit of your function as x → ± ∞ .

Thank you Sammy. After watching some videos regarding this topic and your assistance, I found out that the horizontal asymptotes are y=-1/2, 1/2 and there are no vertical asymptotes. Thank you again.