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

Explanation:

Step1: Rewrite the function

Divide both numerator and denominator by $x$: $f(x)=\frac{3x}{4 - x}=\frac{3}{\frac{4}{x}-1}$.

Step2: Analyze the limit as $x\to\infty$

As $x\to\infty$, $\frac{4}{x}\to0$. Then $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}\frac{3}{\frac{4}{x}-1}=\frac{3}{0 - 1}=- 3$.

Answer:

The graph approaches -3 as x approaches infinity.