Linear/NonLinear Functions

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change, meaning the ratio of the change in the y-value to the change in the x-value is constant.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is a nonlinear function?

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A nonlinear function is a function that does not have a constant rate of change. Its graph is not a straight line and can take various shapes such as curves or circles.

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CCSS.8.F.A.3

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How can you determine if a function is linear or nonlinear from a table of values?

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If the ratio of the change in the y-values to the change in the x-values is constant for all intervals, the function is linear. If this ratio changes, the function is nonlinear.

Tags

CCSS.8.F.A.3

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What does the term 'domain' refer to in a function?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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What does the term 'range' refer to in a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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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?

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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 over 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 the function crosses the y-axis, indicating the value of y when x is zero.

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How can you identify a linear graph?

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A linear graph is identified by its straight line, which indicates a constant rate of change between the x and y values.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

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What is a quadratic function?

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A quadratic function is a type of nonlinear function that can be represented by a polynomial of degree 2, typically in the form y = ax^2 + bx + c.