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 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 a curve or any shape that is not linear.

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CCSS.8.F.A.3

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What is the slope in a linear function?

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The slope (m) in a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

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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 (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

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CCSS.8.EE.B.6

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 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 difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

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CCSS.8.F.A.1

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How can you determine if a graph represents a function?

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You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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What is a table of values in relation to functions?

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A table of values lists pairs of x and y values that represent a function. It helps in identifying whether the function is linear or nonlinear.

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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, which represents a parabola.

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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 = 2x + 3, which represents a straight line.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2