Piecewise Functions

Front

What is a piecewise function?

Back

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

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How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that piece to find the output.

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What does the notation f(x) mean in a piecewise function?

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f(x) represents the output of the function for a given input x.

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What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a piecewise function?

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

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How can you graph a piecewise function?

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To graph a piecewise function, plot each piece of the function according to its defined interval on the x-axis.

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What is the significance of the endpoints in a piecewise function?

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Endpoints determine whether the function includes or excludes certain values in its domain, affecting the continuity of the graph.

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What is a continuous piecewise function?

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A continuous piecewise function is one where the pieces connect without any gaps or jumps at the endpoints.

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What is a discontinuous piecewise function?

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A discontinuous piecewise function has gaps or jumps in its graph, meaning it is not continuous at certain points.

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How do you find the value of f(x) for x < a in a piecewise function?

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Use the expression defined for the interval where x is less than a to find f(x).