Functions & Linearity

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What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Tags

CCSS.8.F.A.1

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How can you determine if a relation is a function?

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A relation is a function if no two ordered pairs have the same first element (input) with different second elements (output).

Tags

CCSS.8.F.A.1

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What does it mean for a function to be linear?

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A linear function is a function that graphs to a straight line, which means it has a constant rate of change.

Tags

CCSS.8.F.A.3

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What is the general form of a linear function?

Back

The general form of a linear function is 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

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What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and may have curves or bends.

Tags

CCSS.8.F.A.3

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What is the slope of a line?

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

Tags

CCSS.8.EE.B.5

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What is the y-intercept?

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The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the linear function f(x) = mx + b.

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What is a vertical line test?

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

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What does it mean for a function to be one-to-one?

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A one-to-one function is a function where each output value is paired with exactly one input value, meaning no two different inputs produce the same output.

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What is a domain 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.