Does the following piecewise function exist?

Question

If a piece wise function has a domain of [-4,-2] U (-2,2) U [1, infinity)

can it also have a restriction of: f(0) = undefined?

The point (-2,2) would have to go through the y-axis correct?

Making part of the domain have to be (-2,0) U (0,2) instead of (-2, 2) correct?

Answer 1

You are correct that, if you want to exclude a point from an interval, you can write it as the union of two intervals that are open on the ends of the point you want to exclude. In other words if you have three numbers such that , and you want to exclude , you can write the resulting set as . There are other notations, such as or , but those are rarely used in precalculus courses, so it might be best to stick with whatever notation you recognize.

Unfortunately, the relation that you have described is not a function.

The intervals and overlap on the interval . Therefore, there will be two values for the relation on that interval.