What does it mean for a function to be piecewise continuous?

A piecewise continuous function is defined as a function that is composed of multiple, distinct segments or expressions, each applicable to a specific interval within its domain. This means that the function can take on different forms depending on the input value, allowing it to accommodate various behaviors in different sections.

For a function to be piecewise continuous, it is essential that it is defined over chunks of its domain where each piece maintains continuity; that is, there should not be any breaks or jumps within each specified segment. However, the function may have finitely many discontinuities at some points, which distinguishes it from being universally continuous.

This particular characteristic is what makes the answer regarding distinct expressions correct, as it captures the essence of how piecewise continuous functions operate by combining multiple functions—each valid in its respective segment—into a single defined function over its overall domain.