Final answer:
A piecewise function in mathematics returns multiple values based on single or multiple conditions. It is defined using different rules or equations for different intervals or subdomains of its input.
Step-by-step explanation:
In mathematics, the function that returns multiple values based on single or multiple conditions is called a piecewise function.
A piecewise function is defined by different rules or equations for different intervals or subdomains of its input. These rules or equations are usually defined using inequalities or logical conditions.
For example, consider the piecewise function f(x) = {x^2 if x < 0, x if 0 <= x <= 2, 4 if x > 2}. This function returns different values based on the value of x: x^2 if x is negative, x if x is between 0 and 2 (inclusive), and 4 if x is greater than 2.
Piecewise functions are frequently used in various branches of mathematics, such as calculus and algebra, to model real-world situations where multiple scenarios or conditions apply.