Linear Functions

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What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Tags

CCSS.8.F.A.1

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What is the domain of a function?

Back

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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What is the range of 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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What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents 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 relation to be a function?

Back

A relation is a function if every input is associated with exactly one output.

Tags

CCSS.8.F.A.1

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique corresponding y-value.

Tags

CCSS.8.F.A.1

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What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is y^2 = x, as each x-value can correspond to two y-values.

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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, typically in the form f(x) = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the slope of a linear function represent?

Back

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

Tags

CCSS.8.EE.B.5

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What does the y-intercept of a linear function represent?

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The y-intercept of a linear function is the point where the graph intersects the y-axis, representing the value of y when x = 0.