question
what is the horizontal asymptote of the graph of ( f(x)=\frac{4 x^{3}+3 x - 1}{6 x^{3}} )?
give your answer in the form ( y = a ).
provide your answer below:

Question

Accepted Answer

# Explanation:
## Step1: Divide each term by $x^{3}$
$$
\begin{align*}
f(x)&=\frac{4x^{3}+3x - 1}{5x^{3}}\
&=\frac{4x^{3}}{5x^{3}}+\frac{3x}{5x^{3}}-\frac{1}{5x^{3}}\
&=\frac{4}{5}+\frac{3}{5x^{2}}-\frac{1}{5x^{3}}
\end{align*}
$$
## Step2: Find the limit as $x\to\pm\infty$
As $x\to\pm\infty$, $\frac{3}{5x^{2}}\to0$ and $\frac{1}{5x^{3}}\to0$

# Answer:
$y = \frac{4}{5}$

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Question

Explanation:

Step1: Divide each term by \(x^{3}\)

Step2: Find the limit as \(x\to\pm\infty\)

Answer: