Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We are given the following function:

$f(x) = \frac{2x}{x - 1}$

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

$\lim_{x \rightarrow \infty} \frac{2x}{x - 1} = \lim_{x \rightarrow \infty} \frac{2x}{x} = \lim_{x \rightarrow \infty} 2 = 2$

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

Answer 2

Answer:

B

Step-by-step explanation:

I got it right