4. Write an equation for the asymptotes of the function $$ c(x)=\frac{1+4 x}{x} $$ Vertical asymptote: Horizontal asymptote:

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Find the vertical asymptotes of $$ (1+4*x)/(x) $$.
Function by following steps:
- step0: Find the vertical asymptotes:
  $$y=\frac{1+4x}{x}$$
- step1: Evaluate the limit:
  $$\lim _{xightarrow 0}\left(\frac{1+4x}{x}ight)$$
- step2: Evaluate the left-hand and the right-hand limits:
  $$\begin{align}&\lim _{xightarrow 0^{-}}\left(\frac{1+4x}{x}ight)\&\lim _{xightarrow 0^{+}}\left(\frac{1+4x}{x}ight)\end{align}$$
- step3: Evaluate the left-hand limit:
  $$\begin{align}&-\infty\&+\infty\end{align}$$
- step4: Limit does not exist:
  $$	extrm{The limit does not exist}$$
- step5: $$x=0$$ is a vertical asymptote$$:$$
  $$\begin{align}&x=0	extrm{ }	extrm{is a vertical asymptote}\end{align}$$
- step6: List all vertical asymptotes of the function:
  $$\begin{align}&x=0\end{align}$$
Find the horizontal asymptotes of $$ (1+4*x)/(x) $$.
Function by following steps:
- step0: Find the horizontal asymptotes:
  $$y=\frac{1+4x}{x}$$
- step1: Evaluate the limits $$\lim _{xightarrow +\infty}\left(yight)$$ and $$\lim _{xightarrow -\infty}\left(yight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{1+4x}{x}ight)\&\lim _{xightarrow -\infty}\left(\frac{1+4x}{x}ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&4\&4\end{align}$$
- step3: The finite values are horizontal asymptotes:
  $$\begin{align}&y=4\end{align}$$
The equation for the asymptotes of the function $$ c(x)=\frac{1+4x}{x} $$ is as follows:

Vertical asymptote: $$ x=0 $$

Horizontal asymptote: $$ y=4 $$
Vertical asymptote: $$ x=0 $$ Horizontal asymptote: $$ y=4 $$

Write an equation for the asymptotes of the function
Vertical asymptote:
Horizontal asymptote:

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Write an equation for the asymptotes of the function Vertical asymptote: Horizontal asymptote: