Linear vs Nonlinear functions

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its graph can be curved or have a more complex shape.

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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 can be identified by its straight line graph, which has a constant slope.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph or any graph that does not form a straight line.

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CCSS.8.F.A.3

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What does it mean for a graph to represent a function?

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A graph represents a function if every input (x-value) has exactly one output (y-value). This can be tested using the vertical line test.

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What is the vertical line test?

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The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

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What is the slope of a linear function?

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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 of a linear function?

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The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of y 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 graph.

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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 to a straight line.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2