which statement describes the behavior of the function f(x)=2x/(1 - x^2)? the graph approaches -2 as x…

Explanation:

Step1: Analyze the limit as x approaches infinity

We want to find $\lim_{x\rightarrow\infty}\frac{2x}{1 - x^{2}}$. Divide both the numerator and denominator by the highest - power of x in the denominator, which is $x^{2}$. So, $\frac{2x}{1 - x^{2}}=\frac{\frac{2x}{x^{2}}}{\frac{1}{x^{2}}-\frac{x^{2}}{x^{2}}}=\frac{\frac{2}{x}}{\frac{1}{x^{2}} - 1}$.

Step2: Evaluate the limit of each term

As $x\rightarrow\infty$, we know that $\lim_{x\rightarrow\infty}\frac{2}{x}=0$ and $\lim_{x\rightarrow\infty}\frac{1}{x^{2}} = 0$. Then $\lim_{x\rightarrow\infty}\frac{\frac{2}{x}}{\frac{1}{x^{2}} - 1}=\frac{0}{0 - 1}=0$.

Answer:

The graph approaches 0 as x approaches infinity.