Question

What are the horizontal asymptotes of the function f of x equals the quotient of the square root of the quantity x squared plus 1 and x?

Answer 1

Given the function

$\dfrac{\sqrt{x^2+1}}{x}$

The two points concerning the domain are:

• The content of a square root must be non-negative
• The denominator can't be zero

Nevertheless, the content of the square root is $x^2+1$, which is always positive, so it's not a problem.

The denominator, which is x, can't be zero, so we can't have $x = 0$

So, the domain of the function is

$D = \{ x \in \mathbb{R}:\ x \neq 0\}$