3.2 Linear vs NonLinear Functions

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What is a linear function?

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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.

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What is a nonlinear function?

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

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How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph. If the graph curves or bends, it is not linear.

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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 value of y increases by a fixed amount. 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 its steepness, 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 graph of the function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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Linear

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Nonlinear

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.