which statement describes the behavior of the function (f(x)=\frac{2x}{1 - x^{2}})?\nthe graph approaches…

which statement describes the behavior of the function (f(x)=\frac{2x}{1 - x^{2}})?\nthe graph approaches - 2 as x approaches infinity.\nthe graph approaches 0 as x approaches infinity.\nthe graph approaches 1 as x approaches infinity.\nthe graph approaches 2 as x approaches infinity.

which statement describes the behavior of the function (f(x)=\frac{2x}{1 - x^{2}})?\nthe graph approaches - 2 as x approaches infinity.\nthe graph approaches 0 as x approaches infinity.\nthe graph approaches 1 as x approaches infinity.\nthe graph approaches 2 as x approaches infinity.

Answer

Explanation:

Step1: Analyze the limit as x approaches infinity.

As (x\rightarrow\infty), we consider the behavior of (f(x)=\frac{2x}{1 - x^{2}}). Divide both the numerator and denominator by (x^{2}). We get (f(x)=\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), (\lim_{x\rightarrow\infty}\frac{2}{x}=0) and (\lim_{x\rightarrow\infty}\frac{1}{x^{2}} = 0). So (\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.