## anonymous one year ago Find the horizontal asymptote of f(x)= x^2+3x-2/x-2

1. anonymous

I appreciate any help

2. anonymous

You sure that is 3x - 2 in numerator and not 3x + 2 ??

3. anonymous

Yes it's in the numerator

4. anonymous

As you can see, degree of numerator is greater than degree of denominator, you will get Slant Asymptote...

5. anonymous

Ok

6. anonymous

Do you know the Long Division Method??

7. anonymous

No :(

8. anonymous

You have to just divide numerator by denominator.. As you do simple division and then find out the quotient..

9. anonymous

Ok so divide x^2+3x-2 by x-2?

10. anonymous

yep...

11. anonymous

Would it be the same as using synthetic division?

12. anonymous

|dw:1437159263381:dw|

13. anonymous

yes, you can do synthetic division too..!!!

14. anonymous

So, $$y = x + 5$$, this is the Slant Asymptote in this case..

15. anonymous

Where degree of numerator is greater than degree of denominator, there is no horizontal asymptote but there is slant asympote, as you can find that by $$y = quotient$$, for that just use Long Division and find the quotient..

16. anonymous

So I got x+1 - (4/x+2) :/

17. anonymous

Wait so the answer is none?

18. anonymous

yes None is the answer for this.. :P

19. anonymous

There is no horizontal asymptote? What a trick question 😅

20. anonymous

Thanks

21. anonymous

I just told how to find slant asymptote equation if you do not have Horizontal asymptote..

22. anonymous

Oh on :) thanks

23. anonymous

Ok :D

24. anonymous

Thanks again bye~

25. anonymous

See, horizontal asymptote means you will get line parallel to x-axis or where y = 0, but if asymptote is not horizontal, then it must be inclined and y $$\ne$$ 0 there, so how to find y there, I just told you that.. :)

26. anonymous

$$\dagger$$ ..