Rewriting a function as a piecewise function means to express it as a combination of two or more functions, each defined on a specific interval of the domain. This allows for the function to have different rules or equations for different parts of the domain.
The domain of a piecewise function is determined by the union of the domains of the individual functions that make up the piecewise function. This means that the domain will include all values that are included in at least one of the individual function's domains.
The purpose of rewriting a function as a piecewise function is to make it easier to understand and work with. It can also make it possible to define a function for a larger set of values, as each individual function may have a more restricted domain than the overall piecewise function.
The range of a piecewise function can be determined by finding the range of each individual function and then combining them. This can be done by graphing the function or by evaluating the function at various points within the domain.
Yes, any function can be rewritten as a piecewise function as long as it has different rules or equations for different parts of the domain. However, some functions may not necessarily need to be rewritten as a piecewise function as they can be easily expressed in other forms.