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: Divide numerator and denominator by x

We have $f(x)=\frac{3x}{4 - x}$. Dividing both numerator and denominator by $x$ (where $x\neq0$), we get $f(x)=\frac{3}{\frac{4}{x}-1}$.

Step2: Find the limit as x approaches infinity

As $x\rightarrow\infty$, $\frac{4}{x}\rightarrow0$. So, $\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}\frac{3}{\frac{4}{x}-1}=\frac{3}{0 - 1}=- 3$.

Answer:

The graph approaches -3 as x approaches infinity.