Linearity and Continuity of Graphs

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What is a discrete function?

Back

A discrete function is one that consists of individual points and is not connected by a line or curve.

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What is a continuous function?

Back

A continuous function is one that can be graphed with a single line or curve, with no breaks or gaps.

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What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, typically in the form y = mx + b.

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What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function that does not graph to a straight line, and can include curves, parabolas, etc.

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How can you determine if a function is discrete or continuous?

Back

You can determine if a function is discrete or continuous by examining its graph: discrete functions have individual points, while continuous functions have connected lines or curves.

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What is the domain of a function?

Back

The domain of a 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 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.

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What is an example of a discrete function?

Back

An example of a discrete function is the number of students in a classroom, as it can only take whole number values.

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What is an example of a continuous function?

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An example of a continuous function is the height of a plant over time, which can take any value within a range.

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What is a piecewise function?

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A piecewise function is a function that has different expressions or rules for different parts of its domain.