Question

Express the function graphed on the axes below as a piecewisefunction1086381048-10

Answer 1

As the problem states, this is a piecewise function.

First, we will deal with the part of the function that is on the right side of the plane.

1. Right side

Notice that it is a line that is continuous towards the +x-direction.

The first thing we need to do is to calculate its domain (for which x's the function is defined).

That white dot means that the function is discontinuous in x=3, so, the domain of this section of the function is:

`D_R=(3,\infty)`

Now, notice that the lines correspond to the function:

`y=f_L(x)=2`

We will keep in mind these 2 results as we will use them to write the final form of the function.

2. Left side

Notice that there is a black dot (in contrast with the white dot on the right side), which means that the function is continuous in x=-3.

Once again, the first thing to do is to calculate the domain of the section of the function:

`D_L=(-\infty,-3\rbrack`

Then, notice that the line on the left side corresponds to the next function:

`y=f_L(x)=-x`

We can reach that result easily after noticing that the points (-3,3) and (-4,4) are in the line.

Summing up the results, we get the function that joins the left side and the right side:

`F(x)=\begin{cases}F(x)=y=2;x>3 \\ F(x)=y=-x;x\le-3\end{cases}`

F(X) is the answer to the problem