## gjhfdfg Group Title Find the vertical asymptotes, if any, of the graph of the rational function. one year ago one year ago

1. gjhfdfg Group Title

f(x)= $\frac{ x }{ x^2 +1 }$

2. jim_thompson5910 Group Title

solve x^2 + 1 = 0 for x

3. jim_thompson5910 Group Title

tell me what you get

4. gjhfdfg Group Title

Would it just be x^2 = -1 ?

5. jim_thompson5910 Group Title

good so far, what's next?

6. k.rajabhishek Group Title

there will be no vertical asymptote

7. gjhfdfg Group Title

Hmm, Im not sure? Do I replace the variable with -1?

8. jim_thompson5910 Group Title

take the square root of both sides x = sqrt(-1) or x = -sqrt(-1) but there's a problem, you can't take the square root of -1 and get a real number

9. jim_thompson5910 Group Title

so x^2 + 1 = 0 has no real solutions

10. jim_thompson5910 Group Title

leading to the fact that $\Large \frac{ x }{ x^2 +1 }$ has no vertical asymptotes

11. gjhfdfg Group Title

Ah, ok. Thank you.! Just out of curiosity, what happened to the x on top of the fraction?

12. jim_thompson5910 Group Title

the numerator doesn't play any role in finding the vertical asymptotes unless you can make it cancel with something in the denominator

13. jim_thompson5910 Group Title

if you had something like x -------- x^2+x the fraction would simplify to 1 ________ x + 1 and this would be a case where the numerator plays a role

14. gjhfdfg Group Title

So basically the numerator was pointless in this equation?

15. jim_thompson5910 Group Title

pretty much

16. jim_thompson5910 Group Title

the basic thing is to simplify as much as possible (which couldn't be done in this case) then look at the denominator only

17. gjhfdfg Group Title

Got it, thank you again.!

18. jim_thompson5910 Group Title

sure thing