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 expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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, bends, or other shapes.

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How can you determine if a function is linear from a table of values?

Back

A function is linear if the ratio of the change in the y-values to the change in the x-values is constant for all pairs of points.

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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, resulting in a straight line on a graph.

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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?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) in the equation y = mx + b.

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Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as x increases, y decreases.

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabolic curve when graphed.

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How can you identify a nonlinear function from a graph?

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A nonlinear function can be identified from a graph by looking for curves or bends; it will not form a straight line.

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What is the difference between a linear equation and a linear function?

Back

A linear equation is an equation that represents a linear relationship, while a linear function is a specific type of linear equation that defines a relationship between x and y.