Linear versus Nonlinear Functions

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What is a linear function?

Back

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.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be curved or have various shapes, and it does not have a constant rate of change.

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CCSS.8.F.A.3

Front

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. If the highest exponent of the variable is 1, it is linear.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify a nonlinear function from its equation?

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A nonlinear function can be identified by equations that include exponents greater than 1, variables multiplied together, or functions like sine, cosine, or exponential functions.

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CCSS.8.F.A.3

Front

What is the slope of a linear function?

Back

The slope of a linear function (m) 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?

Back

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

Front

What is the graph of a linear function?

Back

The graph of a linear function is a straight line that can either be increasing, decreasing, or constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the graph of a nonlinear function?

Back

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

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2 + 2.

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CCSS.8.F.A.3