Piecewise Functions

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What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas over different intervals of its domain.

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How do you determine the domain of a piecewise function?

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To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you find the range of a piecewise function?

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To find the range of a piecewise function, evaluate each piece over its domain and combine the resulting output values.

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What does it mean for a function to behave like a quadratic function?

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A function behaves like a quadratic function if it can be represented by a polynomial of degree 2, typically having a parabolic shape.

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What is the significance of domain restrictions in piecewise functions?

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Domain restrictions indicate the specific values of x for which the function is defined, which can affect the overall behavior and output of the function.

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How do you match a graph to its corresponding piecewise function?

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To match a graph to its corresponding piecewise function, analyze the shape and behavior of the graph in different intervals and compare it to the equations of the piecewise function.

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What is the importance of understanding intervals in piecewise functions?

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Understanding intervals is crucial because each interval may have a different rule or equation that defines the function's behavior.

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What is the notation for representing intervals in mathematics?

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Intervals are often represented using brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.

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How do you express the domain of a piecewise function using interval notation?

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The domain can be expressed in interval notation by combining the intervals for which the function is defined, using union symbols as needed.