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

Key Concepts

Piecewise Functions

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.

Systems of Equations

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, depending on the complexity and nature of the equations involved.

Methods of Solving

There are various methods for solving systems of equations, including graphing, substitution, and elimination. Each method has its advantages depending on the specific problem. For instance, graphing provides a visual representation, while substitution allows for direct solving of one variable in terms of another, making it easier to find solutions in complex systems.