Question

which statement describes the behavior of the function $f(x)=\frac{3x}{4 - x}$?
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.

Explanation:

Step1: Analyze the function at infinity

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

Step2: Find the limit as x approaches infinity

As $x
ightarrow\infty$, $\frac{4}{x}
ightarrow0$. So, $\lim_{x
ightarrow\infty}\frac{3}{\frac{4}{x}-1}=\frac{3}{0 - 1}=- 3$.

Answer:

The graph approaches -3 as x approaches infinity.