Piecewise function
Definition
A piecewise function is a mathematical function that is defined by different formulas or rules for different intervals of the input variable. It consists of multiple "pieces" or sections, each with its own formula.
Analogy
Think of a piecewise function as a playlist on your music streaming app. Each song in the playlist represents a different formula or rule, and depending on where you are in the playlist (input variable), you follow the corresponding formula to get the output.
Related terms
Continuous function: A continuous function is one that can be drawn without lifting your pen from the paper. In other words, there are no breaks, jumps, or holes in its graph.
Discontinuous function: A discontinuous function is one that has at least one break, jump, or hole in its graph. It may have different pieces or sections that are not connected smoothly.
Step function: A step function is a type of piecewise function where each section is constant within its interval and changes abruptly at specific points. It looks like steps on a staircase when graphed.
"Piecewise function" appears in:
Study guides (1)
Practice Questions (1)
- For a piecewise function, what must be true for the function to be continuous at the points where the pieces connect?
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