which of the following describes the end behavior of f(x)=2x/(3x^2 - 3)? the graph approaches 0 as x…

which of the following describes the end behavior of f(x)=2x/(3x^2 - 3)? the graph approaches 0 as x approaches infinity. the graph approaches 0 as x approaches negative infinity. the graph approaches 2/3 as x approaches infinity. the graph approaches -1 as x approaches negative infinity. retry

which of the following describes the end behavior of f(x)=2x/(3x^2 - 3)? the graph approaches 0 as x approaches infinity. the graph approaches 0 as x approaches negative infinity. the graph approaches 2/3 as x approaches infinity. the graph approaches -1 as x approaches negative infinity. retry

Answer

Answer:

The graph approaches 0 as x approaches infinity. The graph approaches 0 as x approaches negative infinity.

Explanation:

Step1: Analyze degree of polynomials

The degree of the numerator $2x$ is 1 and the degree of the denominator $3x^{2}-3$ is 2. Since the degree of the denominator is greater than the degree of the numerator.

Step2: Determine end - behavior

For a rational function $\frac{f(x)}{g(x)}$ where $\text{deg}(g(x))>\text{deg}(f(x))$, as $x\to\pm\infty$, $y = \frac{f(x)}{g(x)}\to0$. So as $x\to\infty$ and $x\to-\infty$, $f(x)=\frac{2x}{3x^{2}-3}\to0$.