Linear vs 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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CCSS.8.F.B.4

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What is a nonlinear function?

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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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CCSS.8.F.A.3

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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 difference between the y-values for equal intervals of x-values. If the differences are not constant, the function is nonlinear.

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CCSS.8.F.B.4

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What does the graph of a linear function look like?

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The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the graph of a nonlinear function look like?

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The graph of a nonlinear function can take various shapes, such as curves, parabolas, or circles, and does not form a straight line.

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CCSS.8.F.A.1

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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 over run).

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CCSS.8.EE.B.5

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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, represented by the value of b in the equation y = mx + b.

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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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CCSS.8.EE.B.5

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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.

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CCSS.8.F.A.3

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

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If the equation can be simplified to the form y = mx + b, it is linear. If it includes variables raised to powers other than one, it is nonlinear.

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CCSS.8.F.A.3