A piecewise function is defined by multiple sub-functions, each applying to a specific interval of the domain. It allows for different behaviors over different parts of the domain.
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Piecewise functions are often used to model situations where a rule changes based on the input value.
The domain of a piecewise function is the union of the domains of its sub-functions.
Each sub-function in a piecewise function has its own formula and interval.
When graphing a piecewise function, you plot each sub-function over its specified interval and check for continuity at the boundaries.
To evaluate a piecewise function, determine which sub-function applies to the given input value.
Review Questions
How do you determine which sub-function to use when evaluating a piecewise function?
What is the significance of domain intervals in defining a piecewise function?
How can you ensure continuity when graphing a piecewise function?
Related terms
Domain: The set of all possible input values (independent variables) for which a function is defined.
Range: The set of all possible output values (dependent variables) that a function can produce.
Interval Notation: A way of writing subsets of the real number line using intervals. It uses brackets and parentheses to describe whether endpoints are included or excluded.