Linear vs 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.

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 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 graph?

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A linear function's graph is a straight line, and it has a constant rate of change.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over 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 is the point where the line crosses the y-axis, representing the value of the function when x = 0.

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

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CCSS.8.F.A.1

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How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of a relation at more than one point, then it is not a function.

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What is 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

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What is an example of a nonlinear function?

Back

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

Tags

CCSS.8.F.A.3

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What does it mean for a function to be increasing?

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A function is increasing if, as x increases, the value of f(x) also increases.