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.

Question

Accepted Answer

# Explanation:
## Step1: Divide numerator and denominator by $x$
Divide numerator $3x$ and denominator $4 - x$ by $x$.
$$
\begin{align*}
\lim_{x
ightarrow\infty}\frac{3x}{4 - x}&=\lim_{x
ightarrow\infty}\frac{\frac{3x}{x}}{\frac{4}{x}-\frac{x}{x}}\
&=\lim_{x
ightarrow\infty}\frac{3}{\frac{4}{x}- 1}
\end{align*}
$$
## Step2: Evaluate the limit
As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{4}{x}=0$.
$$
\begin{align*}
\lim_{x
ightarrow\infty}\frac{3}{\frac{4}{x}- 1}&=\frac{3}{0 - 1}\
&=- 3
\end{align*}
$$

# Answer:
The graph approaches $-3$ as $x$ approaches infinity.

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QUESTION IMAGE

Question

Explanation:

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

Step2: Evaluate the limit

Answer: