Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Inequalities
A system of inequalities consists of two or more inequalities that share the same variables. The solution set is the region where the graphs of these inequalities overlap. Understanding how to graph each inequality and identify the feasible region is crucial for solving these systems.
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Graphing Techniques
Graphing techniques involve plotting inequalities on a coordinate plane. This includes determining boundary lines, using dashed or solid lines to indicate whether points on the line are included, and shading the appropriate regions to represent the solution set. Mastery of these techniques is essential for visualizing and solving systems of inequalities.
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Graphs and Coordinates - Example
Piecewise Functions
A piecewise function is defined by different expressions based on the input value. Understanding how to interpret and graph piecewise functions is important, as they can represent complex relationships in systems of inequalities. Recognizing the conditions under which each piece applies helps in accurately graphing the overall function.
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