Question

What are the domain and range of the piecewise function below? HELP ASAP

Answer 1

The domain is the set of all point where you can evaluate the function.

As you can see, the first piece is defined from -infinity to 2 (included).

The second piece is defined from 2 to 6 (excluded).

The third piece is defined from 6 (excluded) to +infinity.

So, the domain of the function is composed by all the real numbers which are not 6:

As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.

The second piece is constantly equal to 2, so it adds nothing.

The third piece spans the y axis from -2 to -infinity, so the range is

Answer 2

The domain is the set of all point where you can evaluate the function.

As you can see, the first piece is defined from -infinity to 2 (included).

The second piece is defined from 2 to 6 (excluded).

The third piece is defined from 6 (excluded) to +infinity.

So, the domain of the function is composed by all the real numbers which are not 6:

$(-\infty,6)\cup(6,\infty) = \mathbb{R}\setminus\{6\} = \{x \in \mathbb{R}\ :\ x\neq 6\}$

As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.

The second piece is constantly equal to 2, so it adds nothing.

The third piece spans the y axis from -2 to -infinity, so the range is

$(-\infty,-2)\cup[0,\infty) = \mathbb{R}\setminus [2,0) = \{x \in \mathbb{R}\ :\ x\geq 0\ \lor\ x$