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 function's domain. This means that the function can take different forms based on the input value. For example, a piecewise function might be defined as f(x) = x^2 for x < 0 and f(x) = 2x + 1 for x ≥ 0, illustrating how the function behaves differently in different regions.
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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). Understanding the domain and range is crucial for defining piecewise functions, as each piece may have its own specific domain, affecting how the function behaves overall.
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Finding the Domain and Range of a Graph
Graph Interpretation
Interpreting the graph of a function involves analyzing its shape, slopes, and intercepts to understand its behavior. For piecewise functions, the graph may consist of distinct segments, each corresponding to different rules. Recognizing where these segments start and end is essential for accurately defining the function and understanding its continuity and discontinuities.
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