Question

Please solve with as if you didn’t have a calculator

Answer 1

Step-by-step explanation:

For the given function

`f(x)=(1)/((x+3))-2`

We are told to Graph the function

The graph is given below

Thus

The Domain of the function is

`\begin{bmatrix}\mathrm{Solution\colon}\: & \: x<-3\quad \mathrm{or}\quad \: x>-3\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-\infty\: ,\: -3\mright)\cup\mleft(-3,\: \infty\: \mright)\end{bmatrix}`

The Range of the function is

`\begin{bmatrix}\mathrm{Solution\colon}\: & \: f\mleft(x\mright)<-2\quad \mathrm{or}\quad \: f\mleft(x\mright)>-2\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-\infty\: ,\: -2\mright)\cup\mleft(-2,\: \infty\: \mright)\end{bmatrix}`

The Asymptotes are

`\begin{gathered} \mathrm{Vertical}\colon\: x=-3,\: \\ \mathrm{Horizontal}\colon\: y=-2 \end{gathered}`

It is decreasing on

`\mathrm{Decreasing}\colon-\infty\: <p>It is increasing on</p>[tex]\text{None}`

Limits

`\begin{gathered} \lim _(x\Rightarrow3^-)f(x)=-\infty \\ \\ \lim _(x\Rightarrow3^+)f(x)=\infty \end{gathered}`