Piecewise function

Definition

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.

5 Must Know Facts For Your Next Test

1. Piecewise functions are often used to model situations where a rule changes based on the input value.
2. The domain of a piecewise function is the union of the domains of its sub-functions.
3. Each sub-function in a piecewise function has its own formula and interval.
4. When graphing a piecewise function, you plot each sub-function over its specified interval and check for continuity at the boundaries.
5. 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.