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 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 form a straight line when graphed. Its graph can be curved or have varying slopes.

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CCSS.8.F.A.3

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How can you identify a linear function from its equation?

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A linear function can be identified by its equation being in the form y = mx + b, where m and b are constants.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

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CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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Can a function be both linear and nonlinear?

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No, a function cannot be both linear and nonlinear. It is classified as one or the other based on its characteristics.

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CCSS.8.F.A.3

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What is an example of a linear function?

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An example of a linear function is y = 3x + 2.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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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 or y = 1/x.

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CCSS.8.F.A.3

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How do you determine if a function is linear from a graph?

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A function is linear if its graph is a straight line. If the graph curves or has bends, it is nonlinear.

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CCSS.8.F.A.3

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What is the general form of a linear equation in two variables?

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The general form of a linear equation in two variables is Ax + By + C = 0, where A, B, and C are constants.