Linear vs Non-linear

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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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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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 a curve or any shape that is not a straight line.

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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, which is in the form f(x) = mx + b. If the highest exponent of the variable is 1, it is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

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

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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 dependent variable changes for a unit change in the independent variable.

Tags

CCSS.8.EE.B.5

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What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, which occurs when x = 0.

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Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line and the output value remains constant regardless of the input.

Tags

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 f(x) = x^2, which represents a parabolic curve.

Tags

CCSS.8.F.A.3

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How can you determine if a graph represents a linear or nonlinear relationship?

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You can determine if a graph represents a linear or nonlinear relationship by checking if the graph forms a straight line (linear) or a curve (nonlinear).

Tags

CCSS.8.F.A.3

Front

What is the significance of the domain and range in linear functions?

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The domain of a linear function is all real numbers, while the range is also all real numbers, meaning linear functions can take any input and produce any output.