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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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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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 can have curves, bends, or changes in direction, and does not have a constant rate of change.

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CCSS.8.F.A.3

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How can you identify a linear function from its graph?

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A linear function can be identified by its straight line graph. If the graph has a constant slope and does not curve, it is linear.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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How can you identify a nonlinear function from its graph?

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A nonlinear function can be identified by its curved or bent graph. If the graph changes direction or has varying slopes, it is nonlinear.

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CCSS.8.F.A.3

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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. It indicates how much the y-value changes for a given change in the x-value.

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CCSS.8.EE.B.5

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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 crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

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What is the general form of a linear equation?

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The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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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 the x-value increases, the y-value 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 creates a parabolic curve when graphed.

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CCSS.8.F.A.3

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

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A linear equation represents a straight line and has a constant rate of change, while a nonlinear equation represents a curve and has a varying rate of change.

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CCSS.8.F.A.3