Linear vs. Nonlinear Functions

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It has a variable rate of change and can include curves, parabolas, or other shapes.

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How can you identify a linear function from a table of values?

Back

A linear function can be identified from a table of values if the ratio of the change in y to the change in x is constant for all pairs of values.

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What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that for every unit increase in x, the change in y is always the same. This is characteristic of linear functions.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise/run).

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What is the y-intercept of a linear function?

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The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x is 0 in the equation of the line.

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Can a function be both linear and nonlinear?

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No, a function cannot be both linear and nonlinear. It is either one or the other based on its characteristics.

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3, which represents a straight line with a slope of 2 and a y-intercept of 3.

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2, which represents a parabola and does not create a straight line.

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How can you tell if a graph represents a linear function?

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A graph represents a linear function if it forms a straight line. If the graph curves or bends, it is nonlinear.