In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

A piecewise function is defined by multiple sub-functions, each applying to a specific interval of the domain. Understanding how to interpret and evaluate these functions is crucial, as the output depends on the input's range. For example, a function might be defined as f(x) = x^2 for x < 0 and f(x) = 2x + 1 for x ≥ 0, requiring careful consideration of the input value.

A system of equations consists of two or more equations that share common variables. Solving these systems involves finding the values of the variables that satisfy all equations simultaneously. Methods such as substitution, elimination, or graphical representation can be employed, and understanding these techniques is essential for finding solutions in various contexts, including piecewise functions.

There are several methods for solving systems of equations, including graphing, substitution, and elimination. Each method has its advantages depending on the complexity of the equations and the context. For instance, graphing provides a visual representation, while substitution allows for direct calculation of variable values. Familiarity with these methods is vital for effectively tackling problems involving piecewise functions.