Given the graph of a Piecewise Function, you can identify that it has three pieces. See the picture below:
By definition, the open circles indicates that that endpoint is not included in the interval of the function.
By definition, the Domain of a function is the set of all the input values (x-values) for which the function is defined.
In this case, you need to analyze each piece in order to determine its Domain:
1. Notice that piece 1 goes from:
To:
But -2 is not included. Therefore:
2. Notice that piece 2 goes from:
To:
But since its endpoints are not included:
3. Piece 3 goes from:
To:
Since the x-value 6 is not included:
Hence, the answer is:
- For the first piece from left to right:
- For the middle piece:
- For the third piece from left to right: