Question

Which graph represents the function f (x) = StartFraction 2 x Over x squared minus 1 EndFraction?

Answer 1

Answer:

Step-by-step explanation:

f(x) = 2 / (x^2 - 1) is better written as

                 2

f(x) = ------------------

         (x - 1)(x + 1)

This is undefined at x = -1 and x = 1; there are vertical asymptotes at x = -1 and x = 1.

The y-intercept is found by letting x = 0; we get

                 2

f(x) = ------------------ = -2    =>    (0, -2)

         (0 - 1)(0 + 1)

Please, next time, share the answer choices.  Thank you.

Answer 2

By analyzing the asymptotes we can find the graph of the rational function. Also a graph is provided below.

Which graph represents the function?

We have the rational function:

f(x) = (2x)/(x^2 - 1).

First, you can see that we have two zeros on the denominator. One happens when x = 1 and the other when x = -1.

This means that the graph of this function will have two vertical asymptotes at these values. (four actually as we have one going to each end in each point).

With that description we can find the graph of the function, I will also post it so you can recognize it.

If you want to learn more about rational functions, you can read:

https://brainly.com/question/1851758