Question

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

Answer 1

It's B

Explanation:

took the test, hope this helps!

Answer 2

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

Explanation:

We are given the following function:

`f(x) = (2x)/(x - 1)`

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

`\lim_(x \rightarrow \infty) (2x)/(x - 1) = \lim_(x \rightarrow \infty) (2x)/(x) = \lim_(x \rightarrow \infty) 2 = 2`

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

`x - 1 = 0 \rightarrow x = 1`

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

The correct option is:

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