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 has a variable rate of change and can include curves, parabolas, and other shapes.

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

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

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of the function, indicating how much the y-value changes for a unit change in the x-value.

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What is the y-intercept of a linear function?

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The y-intercept of a linear function is the point where the graph intersects the y-axis, represented as (0, b) in the equation y = mx + b.

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What is the difference between a linear and a nonlinear graph?

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A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

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What does it mean if a function has a constant rate of change?

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If a function has a constant rate of change, it means that for every unit increase in x, the change in y is always the same, indicating a linear relationship.

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Can a linear function have a negative slope?

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

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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 creates a parabolic curve when graphed.

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How do you determine if a function is linear or nonlinear from its equation?

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To determine if a function is linear or nonlinear from its equation, check if it can be written in the form y = mx + b. If it cannot, it is nonlinear.