Linear vs Non Linear 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

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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CCSS.8.F.A.3

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How can you identify a linear equation from a set of equations?

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A linear equation can be identified by its degree (which is 1) and its graph, which will always be a straight line. It can be expressed in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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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, represented by 'm' in the equation y = mx + b. It indicates the change in y for a unit change in x.

Tags

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 graph of the function crosses the y-axis. It is represented by 'b' in the equation y = mx + b.

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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). In contrast, a relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

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What is an ordered pair in the context of functions?

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An ordered pair is a pair of numbers (x, y) that represents a point on a graph, where 'x' is the input and 'y' is the output of a function.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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How can you determine if a set of points represents a linear function?

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To determine if a set of points represents a linear function, check if the differences in y-values divided by the differences in x-values (slopes) are constant for all pairs of points.

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CCSS.HSF-LE.A.1B

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What is a table of values in relation to functions?

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A table of values is a systematic way of displaying pairs of input and output values for a function, which can help in identifying the nature of the function (linear or nonlinear).

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What is the significance of a nonlinear function in real-world applications?

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Nonlinear functions are significant in real-world applications as they can model complex relationships where changes in one variable do not result in proportional changes in another.