which statement describes the behavior of the function f(x)=3x/(4 - x)? the graph approaches - 3 as x…

which statement describes the behavior of the function f(x)=3x/(4 - x)? the graph approaches - 3 as x approaches infinity. the graph approaches 0 as x approaches infinity. the graph approaches 3 as x approaches infinity. the graph approaches 4 as x approaches infinity.

which statement describes the behavior of the function f(x)=3x/(4 - x)? the graph approaches - 3 as x approaches infinity. the graph approaches 0 as x approaches infinity. the graph approaches 3 as x approaches infinity. the graph approaches 4 as x approaches infinity.

Answer

Answer:

A. The graph approaches -3 as x approaches infinity.

Explanation:

Step1: Rewrite the function

$f(x)=\frac{3x}{4 - x}=\frac{-3(-x)}{4 - x}=\frac{-3(4 - x+4)}{4 - x}=-3-\frac{12}{4 - x}$

Step2: Analyze the limit as x approaches infinity

As $x\rightarrow\infty$, $\frac{12}{4 - x}\rightarrow0$. So, $\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}(-3-\frac{12}{4 - x})=-3$.