Linear vs Non-Linear

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. 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 form a straight line when graphed. The rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

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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 (the slope) is constant for all pairs of values.

Front

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

Back

A nonlinear function can be identified from a table of values if the ratio of the change in y to the change in x is not constant.

Front

What does the slope of a linear function represent?

Back

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

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What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x is 0.

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Can a linear function have a negative slope?

Back

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

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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What is an example of a nonlinear equation?

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An example of a nonlinear equation is y = x^2, which represents a parabola.

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What is the significance of a function being linear or nonlinear?

Back

The significance lies in how the function behaves; linear functions have predictable, constant rates of change, while nonlinear functions can exhibit more complex behavior.