Linear or 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.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its 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 determine if a function is linear from a table of values?

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To determine if a function is linear from a table, check if the differences between consecutive y-values are constant when the x-values increase by the same amount.

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

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If a function is represented by a straight line on a graph, it indicates that the function is linear, meaning it has a constant rate of change.

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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 its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

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What is the y-intercept in a linear function?

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The y-intercept is the point where the graph of a linear function crosses the y-axis. It is the value of y when x is 0.

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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 means 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 represents a parabola and does not form a straight line.

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

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A linear equation can be written in the form y = mx + b, while a nonlinear equation may include variables raised to powers other than one, such as y = x^2 or y = sin(x).

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How do you identify a nonlinear relationship from a graph?

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A nonlinear relationship can be identified from a graph if the plotted points do not form a straight line and instead create curves or other shapes.