Question

piecewise function formula from graph | functions and their graphs | algebra ii | khan academy
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open-ended question
why do you think it is called a piecewise function?
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Explanation:

A piecewise function is called so because its definition is given by multiple "pieces" or sub - functions, each of which applies to a different interval of the domain. Looking at the graph, we can see that the function's graph is composed of separate line segments (pieces), each segment corresponding to a different part of the domain. For example, there are different vertical or horizontal (or slanted) line segments that are defined over different intervals on the x - axis. So, it is called piecewise as it is made up of multiple pieces (sub - functions) defined on different intervals.

Answer:

A piecewise function is called so because it is defined by multiple "pieces" (sub - functions), each applying to a different interval of the domain, as seen in the graph with separate line segments (pieces) over different x - intervals.