A piecewise function is defined by multiple sub-functions, each applying to a specific interval of the domain. Graphing them can be tricky because you need to pay close attention to the endpoints of these intervals and whether they are included or excluded.
The biggest mistake is incorrectly plotting the endpoints or not paying attention to whether the endpoint is included (closed circle) or excluded (open circle) in the interval. This affects the functions value at that point and its continuity.
Use a closed circle if the endpoint is included in the interval (≤ or ≥). Use an open circle if the endpoint is excluded from the interval (< or >).
If two pieces overlap, carefully evaluate the function at that specific point for each piece. Only one piece can define the functions value at that point. If both pieces define the function at that point, it may not be a function.
Pay very close attention to the inequality signs (>,