Identifying 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).

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What does it mean for a relation to NOT be a function?

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A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

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How can you identify a function from a graph?

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A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

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What is the Vertical Line Test?

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The Vertical Line Test states that if a vertical line crosses a graph more than once, the graph does not represent a function.

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What is an example of a function?

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An example of a function is the equation y = 2x + 3, where each x-value has a unique y-value.

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

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An example of a relation that is not a function is the set of points {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

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What does a mapping diagram show?

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A mapping diagram visually represents how each input (x) is paired with an output (y). If any input is paired with more than one output, it is not a function.

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How can you tell if a table represents a function?

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A table represents a function if each x-value appears only once in the table.

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What is the definition of a domain in 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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What is the definition of a range in 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.