Identify the asymptotes. Give your answers in exact form. Do not round.

Separate multiple equations of asymptotes with commas as necessary. Select “None” if appli
Part 1 of 2

Ask by Bates Huff. in the United States

Nov 09,2024

Question

Identify the asymptotes. Give your answers in exact form. Do not round.

Separate multiple equations of asymptotes with commas as necessary. Select “None” if appli
Part 1 of 2

Ask by Bates Huff. in the United States

Nov 09,2024

UpStudy AI · Accepted Answer

Find the horizontal asymptotes of the function $$ f(x)=\frac{-3x^2-5}{x} $$.
Function by following steps:
- step0: Find the horizontal asymptotes:
  $$f\left(xight)=\frac{-3x^{2}-5}{x}$$
- step1: Evaluate the limits $$\lim _{xightarrow +\infty}\left(f\left(xight)ight)$$ and $$\lim _{xightarrow -\infty}\left(f\left(xight)ight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{-3x^{2}-5}{x}ight)\&\lim _{xightarrow -\infty}\left(\frac{-3x^{2}-5}{x}ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&-\infty\&+\infty\end{align}$$
- step3: The function has no horizontal asymptotes:
  $$	extrm{No horizontal asymptotes}$$
Find the vertical asymptotes of the function $$ f(x)=\frac{-3x^2-5}{x} $$.
Function by following steps:
- step0: Find the vertical asymptotes:
  $$f\left(xight)=\frac{-3x^{2}-5}{x}$$
- step1: Evaluate the limit:
  $$\lim _{xightarrow 0}\left(\frac{-3x^{2}-5}{x}ight)$$
- step2: Evaluate the left-hand and the right-hand limits:
  $$\begin{align}&\lim _{xightarrow 0^{-}}\left(\frac{-3x^{2}-5}{x}ight)\&\lim _{xightarrow 0^{+}}\left(\frac{-3x^{2}-5}{x}ight)\end{align}$$
- 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:
  $$\begin{align}&x=0\end{align}$$
The vertical asymptote of the function $$ f(x)=\frac{-3x^2-5}{x} $$ is $$ x=0 $$.

Therefore, the asymptotes of the function are $$ x=0 $$.
The asymptotes are $$ x=0 $$.

Identify the asymptotes. Give your answers in exact form. Do not round.

Separate multiple equations of asymptotes with commas as necessary. Select “None” if appli
Part 1 of 2

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Calculus Questions

Identify the asymptotes. Give your answers in exact form. Do not round. Separate multiple equations of asymptotes with commas as necessary. Select “None” if appli Part 1 of 2

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Calculus Questions

Identify the asymptotes. Give your answers in exact form. Do not round.

Separate multiple equations of asymptotes with commas as necessary. Select “None” if appli
Part 1 of 2