Piecewise Functions
A piecewise function is usually defined by parts or pieces, where each piece is defined in a specific interval of x.
The figure provided has a graph where three pieces of a function are clearly visible.
The first piece is a flat horizontal line that runs from x = -6 and x = -2, both included. The filled circle indicates the endpoint is included, thus the interval for this first piece is: [-6, -2], or equivalently:
-6 ≤ x ≤ -2
The second piece is another flat horizontal line that runs from x = -2 (not included) and x = 1 (included). The interval for this part is (-2, 1] or equivalently:
-2 < x ≤ 1
The final part is a horizontal line that runs from x = 1 (not included) to x = 5 (included). The interval for this piece is (1, 5], or equivalently:
1 < x ≤ 5