Linear vs Nonlinear functions

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What is the definition of a linear function?

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A linear function is a function that can be graphically represented as a straight line, characterized by 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 definition of a nonlinear function?

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A nonlinear function is a function that does not have a constant rate of change and cannot be represented as a straight line on a graph.

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CCSS.8.F.A.3

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How can you determine if a function is linear based on a table of values?

Back

A function is linear if the ratio of the change in the y-values to the change in the x-values is constant for all intervals.

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CCSS.HSF-LE.A.1B

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What is the significance of the slope in a linear function?

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The slope represents the rate of change of the function, indicating how much the y-value changes for a unit change in the x-value.

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CCSS.8.EE.B.5

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

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A graph represents a function if every x-value corresponds to exactly one y-value, which is known as the vertical line test.

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What is the vertical line test?

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The vertical line test is a method to determine if a graph represents a function; if any vertical line intersects the graph at more than one point, it is not a function.

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What are some common forms of linear equations?

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Common forms of linear equations include slope-intercept form (y = mx + b) and standard form (Ax + By = C).

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What is the general shape of a graph representing a nonlinear function?

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Nonlinear functions can have various shapes, including curves, parabolas, and other non-straight line forms.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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How can you identify a linear function from a graph?

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A linear function can be identified by its straight-line graph, which has a constant slope and does not curve.

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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?

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An example of a nonlinear function is a quadratic function, such as y = x^2, which produces a parabolic graph.

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CCSS.8.F.A.3