Functions vs Non-Functions

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What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Tags

CCSS.8.F.A.1

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What is a relation?

Back

A relation is a set of ordered pairs, which can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

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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 result from the function.

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What is the domain of a function?

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The domain of a function is the set of all possible input values (x-values) that the function can accept.

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How can you determine if a relation is a function?

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You can use the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

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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 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 {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Tags

CCSS.8.F.A.1

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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 is produced by exactly one input.

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What is a linear function?

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A linear function is a function that graphs to 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 is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax^2 + bx + c, where a ≠ 0.