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 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?

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?

Back

A linear function's graph is a straight line, and it passes the vertical line test, meaning any vertical line intersects the graph at most once.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line crosses the graph more than once, it is not a function.

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What does it mean for y to be a function of x?

Back

It means that for every input value of x, there is exactly one output value of y.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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CCSS.8.EE.B.5

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What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

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Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. This would violate the definition of a function.

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CCSS.8.F.A.1

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line when graphed.

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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, which represents a parabola when graphed.

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CCSS.8.F.A.3