Question

Please show work as if you don’t have a calculator

Answer 1

Given:

There are given that the function:

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

Step-by-step explanation:

The graph of the given function is shown below:

Now,

(1) Domain:

To find the domain of the given function, we need to find the value where the function is defined.

Then,

The domain of the given function is:

`\text{Domain: (-}\infty,-3)\cup(-3,\infty)`

(2) Range:

To find the range of the given function, we need to find the set of values that correspond with the domain.

So,

The range of the given function is:

`(-\infty,-2)\cup(-2,\infty)`

(3) Increasing on:

`\text{ increasing on: never increasing}`

(4) Decreasing on:

The value of decreasing on:

`(-\infty,-3),(-3,\infty)`

(5): All asymptote:

The value of asymptote are:

`\begin{gathered} \text{vertical asymptote : x=-3} \\ \text{Horizontal asymptote : y=-2} \end{gathered}`

(6) All limit (4):

`\begin{gathered} f(x)=(1)/((x+3))-2 \\ f(4)=(1)/((4+3))-2 \\ f(4)=(1)/(7)-2 \\ f(4)=(-13)/(7) \end{gathered}`

Hence, the all limit at 4 is -1.85.