Linearity and Continuity of Graphs

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What is a linear function?

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A linear function is a function that can be graphed as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a nonlinear function?

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A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve or any other shape that is not a straight line.

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What does it mean for a function to be discrete?

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A discrete function consists of distinct, separate values. Its graph is made up of individual points rather than a continuous line.

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What does it mean for a function to be continuous?

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A continuous function has no breaks, jumps, or holes in its graph. It can be drawn without lifting the pencil from the paper.

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What is the difference between discrete and continuous functions?

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Discrete functions consist of separate points, while continuous functions form a smooth line or curve without breaks.

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What is an example of a discrete function?

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An example of a discrete function is the number of students in a classroom, as you cannot have a fraction of a student.

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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, as it can take on any value within a range.

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What does it mean for a function to be neither discrete nor continuous?

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A function that is neither discrete nor continuous has sections that are continuous but does not form a single line or curve.

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How can you determine if a function is linear or nonlinear?

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You can determine if a function is linear or nonlinear by examining its graph. If it forms a straight line, it is linear; if it curves, it is nonlinear.

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What is the significance of the slope in a linear function?

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The slope (m) in a linear function indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.