Question

How to find the horizontal asymptotes of x+sqrt(x^2 +6(abs x) +4)?

Answer 1

The derivative of |x|= sign(x)
That is the hyperbolic sin function.
From that point are you able to take the derivative of the expression?

Answer 2

Or alternatively you can take the derivative for when x<0 and when x>0 ie\[\frac{ dy }{ dx }x+\sqrt{x ^{2}+6x+4}, x \ge 0\]\[\frac{ dy }{ dx }x+\sqrt{x ^{2}-6x+4}, x < 0\] horizontal asymptotes are when the derivative = 0

Answer 3

Riiiight. Okay, I think I get it... Thank you!

Answer 4

Sure no problem.