Question

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

Answer 1

The answer is B) the graph approaches 0 as x approaches infinity. <span />

Answer 2

Answer:

The graph approaches 0 as x approaches infinity.

B is correct.

Step-by-step explanation:

Given: $f(x)=\dfrac{2x}{1-x^2}$

We need to find the behavior of the function.

End Behavior of function f(x)

$x\rightarrow \infty$

$y=\lim_{x\rightarrow \infty}f(x)$

$y=\lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2}$

$y=\lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2-1}$

$y=\dfrac{2/\infty}{1/\infty-1}$

$y=\dfrac{0}{0-1}$

$y=0$

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.