Question

What is the horizontal asymptote of `f(x) = (-5x)/(sqrt(16x^2 + 7))`?

Answer 1

`y=+-5/4`. A Socratic graph shows the curve and the asymptotes.

Explanation:

`y=f(x)=-(5x)/sqrt(16x^2+7)`

`=-(5x)/((+-x)sqrt(16+7/x^2)`

`=+-5/sqrt(16+7/x^2)`

`to +-5/4`, as `x to +-oo`.

So, `y = +-5/2` give horizontal asymptotes.

graph{(y+(5x)/sqrt(16x^2+7))(y-5/4)(y+5/4)=0 [-1, 1, -2.5, 2.5]}