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.

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.

Answer

Answer:

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

Explanation:

Step1: Identify the degrees of numerator and denominator

The degree of numerator $n = 1$ (for $2x$), degree of denominator $m=2$ (for $3x^{2}-3$).

Step2: Recall the rule for end - behavior of rational functions

When $n<m$, $\lim_{x\rightarrow\pm\infty}\frac{f(x)}{g(x)} = 0$. Here $f(x)=2x$ and $g(x)=3x^{2}-3$. So $\lim_{x\rightarrow\infty}\frac{2x}{3x^{2}-3}=0$ and $\lim_{x\rightarrow-\infty}\frac{2x}{3x^{2}-3}=0$.