finding domain, range, asymptotes of 2x/sqrt(x^2+x+1)

[rioean17]

find the domain, range, horizontal and vertical asymptotes of:

. . .f(x) = 2x/sqrt(x^2 + x + 1)

I know how to find the domain and vertical asymptotes but for some reason I'm having a hard time finding them. Please help! Thank you!

 

[galactus]

That's because it has no vertical asymptote.

The domain is \(\displaystyle (-\infty,\infty)\)

 

[rioean17]

ok thats what i thought, then how do i find the range and horizontal asymptotes

 

[stapel]

ok thats what i thought, then how do i find the range and horizontal asymptotes

For the horizontal asymptotes, try the trick described in your other post: divide through by x, top and bottom.

The range is usually approximated by looking at the graph. Have you learned about any other techniques in your class?

Thank you.

Eliz.