which statement describes the behavior of the function $f(x)=\\frac{3x}{4 - x}$?\nthe graph approaches $-3$…

which statement describes the behavior of the function $f(x)=\\frac{3x}{4 - x}$?\nthe graph approaches $-3$ as $x$ approaches infinity.\nthe graph approaches $0$ as $x$ approaches infinity.\nthe graph approaches $3$ as $x$ approaches infinity.\nthe graph approaches $4$ as $x$ approaches infinity.

which statement describes the behavior of the function $f(x)=\\frac{3x}{4 - x}$?\nthe graph approaches $-3$ as $x$ approaches infinity.\nthe graph approaches $0$ as $x$ approaches infinity.\nthe graph approaches $3$ as $x$ approaches infinity.\nthe graph approaches $4$ as $x$ approaches infinity.

Answer

Answer:

The graph approaches -3 as x approaches infinity.

Explanation:

Step1: Simplificar la función

$$ \begin{align*} f(x)&=\frac{3x}{4 - x}\ &=\frac{3x}{-x + 4}\ &=\frac{3x}{-x(1-\frac{4}{x})}\ &=\frac{3}{-(1-\frac{4}{x})} \end{align*} $$

Step2: Calcular el límite cuando (x\to\infty)

$$ \begin{align*} \lim_{x\to\infty}f(x)&=\lim_{x\to\infty}\frac{3}{-(1-\frac{4}{x})}\ &=\frac{3}{-(1 - 0)}\ &=- 3 \end{align*} $$ Cuando (x\to\infty), (\frac{4}{x}\to0), entonces el límite de (f(x)) es (-3).