Family of functions in AP Calculus AB/BC

Definition

A family of functions refers to a group of related functions that differ only by a constant. Each function in the family shares the same derivative, but they may have different values at specific points.

Related terms

Constant of integration: The constant term that appears when finding antiderivatives. It represents the different possible starting points within a family of functions.

Particular solution: A specific member or function within a family of functions that satisfies additional conditions or constraints given by initial values or boundary conditions.

Arbitrary constant: Another term for the constant of integration. It represents an undetermined value that can take any real number within a given context.