## Anachronism 4 years ago Identify the Horizontal Asymptotes of g(x) = (3x+2)/((x^2)+4)^(1/2))

1. Anachronism

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2. tdabboud

The answer is at 3 and -3

3. Anachronism

how would I go about finding those answers? :/ my teacher hasn't taught us how to find it with radicals in the denominator, so I'm lost.

4. tdabboud

well you look at the ratio of the exponents. The numerator is 3x and the denomintor will just be x. it is x^(2*1/2) = x so the ratio is just 3x/x. As x goes to infinity you get a horizontal asymptote of 3 As x goes to negative infinity you get a horizontal asymptote of -3

5. Anachronism

Thank you so much!

6. tdabboud

understand? I know it probably sounds very confusing

7. Anachronism

I kind of get it, but would it just be 3, then because if I substitute a large negative number for x it is a negative over a negative, and I would still get a positive 3

8. Asanka

if you know how to differentiate it , then differentiate it w.r.t x and equate the answer to 0

9. tdabboud

i dont think she is at that type of math yet, that will be too complex at this point

10. Asanka

yeah

11. Asanka

sorry guys i am new to this so i do not know your standards

12. tdabboud

No the answer will be -3 as you approach -infinity because you need to take into account the ratio 3/1

13. tdabboud

the top will outdo the bottom in this case, a very large negative number times 3 will approach -3 faster then the denomnator will reduce it to 3. Understand? it is confusing but take a second to think about it

14. Anachronism

It's alright, thank you for trying to explain it to me Asanka. I think I just visualized it, and it seems to make sense if the numerator is going three times as fast. Thanks a lot for all your help :)

15. tdabboud

exactly you got it! anytime

16. tsegu_k

I am attaching the solution hoping it will help

17. tdabboud

Nice work! very neat.. but you can just look at the ratio of like exponents to make it a little easier, but either way nice job

18. tsegu_k

Thank you very much