Linear versus 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 f(x) = mx + b, where m is the slope and b is the y-intercept.

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CCSS.HSF.LE.A.2

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 take various forms such as quadratic, exponential, or logarithmic.

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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 will graph as a straight line. It will have a constant slope and will not curve.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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How can you identify a nonlinear function from its graph?

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A nonlinear function will graph as a curve or a line that changes direction. It does not have a constant slope.

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CCSS.8.F.A.3

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What is the slope of a linear function?

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

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CCSS.8.EE.B.5

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

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The y-intercept (b) of a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

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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 f(x) = 2x + 3, which graphs as a straight line.

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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 f(x) = x^2, which graphs as a parabola.

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CCSS.8.F.A.3

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What is the definition of a function?

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A function is a relation that assigns exactly one output (y) for each input (x).

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CCSS.8.F.A.1