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 4 as ( x ) approaches infinity.
the graph approaches 3 as ( x ) approaches infinity.
the graph approaches 0 as ( x ) approaches infinity.

Explanation:

Step1: Divide numerator and denominator by \(x\)

$$
LATEXBLOCK0
$$

Step2: Evaluate the limit

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.