Here are the essential concepts you must grasp in order to answer the question correctly.
Piecewise Functions
A piecewise function is defined by multiple sub-functions, each applying to a specific interval of the domain. This means that the function can have different expressions based on the input value. For example, a piecewise function might be defined differently for x < -2, -2 ≤ x < 0, and x ≥ 0, allowing for varied behavior across its domain.
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Domain and Range
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). For piecewise functions, determining the domain and range involves analyzing each piece of the function to see where it is valid and what outputs it produces.
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Graph Interpretation
Interpreting the graph of a piecewise function involves understanding how the function behaves visually across different intervals. Key points, such as where the function changes from one piece to another, are crucial for identifying the rules governing each segment. The graph provides insight into the function's continuity, slopes, and specific values at given points.
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