What are the vertical and horizontal asymptotes of f (x) = StartFraction 2 x Over x minus 1 EndFraction? horizontal asymptote at y = 0, vertical asymptote at x = 1
horizontal asymptote at y = 2, vertical asymptote at x = 1
horizontal asymptote at y = 1, vertical asymptote at x = 0
horizontal asymptote at y = 1, vertical asymptote at x = 2

horizontal asymptote at y = 2, vertical asymptote at x = 1

Step-by-step explanation:

We are given the following function:

Horizontal asymptote:

The horizontal asymptote of a function is the limit of the function as the input, in this case x, goes to infinity. When we want to find the limit of x going to infinity of a fraction we consider the term with the largest exponent on both the numeration and the denominator. So

So there is a horizontal asymptote at y = 2

Vertical asymptote:

Vertical asymptotes happens at points outside the function domain.

In this question, we have a fraction, in which the denominator cannot be 0. So

Thus, there is a vertical asymptote at x = 1.

The correct option is:

horizontal asymptote at y = 2, vertical asymptote at x = 1