Functions, Domain, and Range

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What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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?

Back

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

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How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test.

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What is a linear function?

Back

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 form a straight line when graphed. Examples include quadratic functions, exponential functions, and trigonometric functions.

Tags

CCSS.8.F.A.3

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What does it mean for a function to be positive?

Back

A function is positive when its output values (y-values) are greater than zero for the given input values (x-values).

Tags

CCSS.HSF.IF.B.4

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What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If a vertical line intersects the curve at more than one point, the curve is not a function.

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

Back

The relation {(1,-5), (-1,6), (1,5), (6,-3)} is not a function because the input 1 corresponds to two different outputs (-5 and 5).

Tags

CCSS.8.F.A.1

Front

What is the significance of the x-intercept of a function?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis, indicating the value of x when the output (y) is zero.