Solve each system in Exercises 12–13. The is a piecewise function

Key Concepts

Piecewise Functions

A piecewise function is defined by multiple sub-functions, each applying to a specific interval of the function's domain. This means that the function can have different expressions based on the input value. Understanding how to evaluate piecewise functions is crucial for solving problems that involve them, as it requires determining which piece of the function to use based on the given input.

Systems of Equations

A system of equations consists of two or more equations that share common variables. The goal is to find the values of these variables that satisfy all equations simultaneously. Solving systems can involve various methods, such as substitution, elimination, or graphing, and is essential for understanding how different equations interact with one another.

Graphing

Graphing is the visual representation of equations or functions on a coordinate plane. It helps in understanding the behavior of functions, including piecewise functions, by illustrating how they change across different intervals. For systems of equations, graphing can provide insights into the solutions, such as identifying points of intersection that represent the solutions to the system.