Identifying Linear and Nonlinear Functions

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What is a linear function?

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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.

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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 terms such as x^2, x^3, or other non-linear expressions.

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

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A linear function will have a constant rate of change between the x and y values. This means that the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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

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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?

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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 b in the equation y = mx + b.

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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. This function has a constant 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. This function creates a parabolic curve when graphed.

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How can you tell if a function is nonlinear from its equation?

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If the equation includes variables raised to a power other than one, or includes products of variables, it is likely nonlinear. For example, y = x^2 is nonlinear.

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What does it mean if a function is represented by a curve on a graph?

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If a function is represented by a curve, it indicates that the function is nonlinear, as linear functions produce straight lines.