Consider the following function. $($If an answer does not exist, enter DNE.$)$

$f(x)=1+\frac{7}{x}-\frac{4}{x^2}$

$($a$)$ Find the vertical asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$x=$

Find the horizontal asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$y=$

$($b$)$ Find the interval$($s$)$ of increase. $($Enter your answer using interval notation.$)$

Find the interval$($s$)$ of decrease. $($Enter your answer using interval notation.$)$

$($c$)$ Find the local maximum and minimum values.

local maximum value

local minimum value

$($d$)$ Find the interval$($s$)$ on which $f$ is concave up$.($Enter your answer using interval notation.$)$

$(\frac{48}{7},)$

Find the interval$($s$)$ on which $f$ is concave down. $($Enter your answer using interval notation.$)$

Find the inflection point.

$(x,y)=()$

$($e$)$ Use the information from parts $($a$)-($d$)$ to sketch the graph of $f.$

$($e$)$ Use the information from parts $($a$)-($d$)$ to sketch the graph of $f.$

Consider the following function. $($If an answer does not exist, enter DNE.$)$

$f(x)=1+\frac{7}{x}-\frac{4}{x^2}$

$($a$)$ Find the vertical asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$x=$

Find the horizontal asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$y=$

$$

$($b$)$ Find the interval$($s$)$ of increase. $($Enter your answer using interval notation.$)$

$(0,\frac{8}{7})$

Find the interval$($s$)$ of decrease. $($Enter your answer using interval notation.$)$

$($c$)$ Find the local maximum and minimum values.

$[$:$\frac{65}{16}\}$

local minimum value

$($d$)$ Find the interval$($s$)$ on which $f$ is concave up$.($Enter your answer using interval notation.$)$

Find the interval$($s$)$ on which $f$ is concave down. $($Enter your answer using interval notation.$)$

$$

Find the inflection point.

$($e$)$ Use the information from parts $($a$)-($d$)$ to sketch the graph of $f.$

$y$

$pH,y$

$1010$

Consider the following function. $($If an answer does not exist, enter DNE.$)$

$f(x)=1+\frac{7}{x}-\frac{4}{x^2}$

$($a$)$ Find the vertical asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$x=$ Find the horizontal asymptote$($s$).($Enter your answers as a comma$-$separated list.$)$

$y=$

$($b$)$ Find the interval$($s$)$ of increase. $($Enter your answer using interval notation.$)$

Find the interval$($s$)$ of decrease. $($Enter your answer using interval notation.$)$

$$

$($c$).$ Find the local maximum and minimum values.

local maximum value $$

local minimum value $$

$($d$)$ Find the interval$($s$)$ on which $f$ is concave up$.($Enter your answer using interval notation.$)$

Find the interval$($s$)$ on which $f$ is concave down. $($Enter your answer using interval notation.$)$

Find the inflection point.

$($e$)$ Use the information from parts $($a$)-($d$)$ to sketch the graph of $f.$