Question

Which statement describes the behavior of the function f(x)= 2x/1-x^2 ?

A.)The graph approaches -2 as x approached infinity
B.)The graph approaches 0 as x approaches infinity
C.)The graph approaches 1 as x approaches infinity
D.)The graph approaches 2 as x approaches infinity

Answer 1

b. The graph approaches 0 as x approaches infinity.

Explanation:

e2021

Answer 2

The graph approaches 0 as x approaches infinity.

B is correct.

Explanation:

Given:
`f(x)=(2x)/(1-x^2)`

We need to find the behavior of the function.

End Behavior of function f(x)

`x\rightarrow \infty`

`y=\lim_(x\rightarrow \infty)f(x)`

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

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

`y=(2/\infty)/(1/\infty-1)`

`y=(0)/(0-1)`

`y=0`

Therefore,

If x approaches to infinity,
`x\rightarrow \infty`

then y approaches to 0,
`y\rightarrow 0`

Hence, The graph approaches 0 as x approaches infinity.