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

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

Explanation:

Step1: Analizar el límite cuando x tiende a infinito

Calculamos $\lim_{x\rightarrow\infty}\frac{3x}{4 - x}$. Dividimos numerador y denominador por $x$: $\lim_{x\rightarrow\infty}\frac{3x/x}{(4 - x)/x}=\lim_{x\rightarrow\infty}\frac{3}{\frac{4}{x}-1}$.

Step2: Evaluar el límite de los términos individuales

Sabemos que $\lim_{x\rightarrow\infty}\frac{4}{x}=0$. Entonces, $\lim_{x\rightarrow\infty}\frac{3}{\frac{4}{x}-1}=\frac{3}{0 - 1}=- 3$.

Answer:

The graph approaches -3 as x approaches infinity. (La gráfica se aproxima a -3 cuando x tiende a infinito)