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: Analyze the limit as x approaches infinity

We find $\lim_{x\rightarrow\infty}\frac{3x}{4 - x}$. Divide both numerator and denominator by $x$: $\lim_{x\rightarrow\infty}\frac{3x/x}{(4 - x)/x}=\lim_{x\rightarrow\infty}\frac{3}{\frac{4}{x}-1}$.

Step2: Evaluate the limit of the denominator terms

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

Answer:

The graph approaches -3 as x approaches infinity.