Determine if Function

Front

What is a function?

Back

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

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How can you determine if a graph represents a function?

Back

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 does it mean if a relation is not a function?

Back

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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What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

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If a relation has the pairs (2, 3), (2, 4), (3, 5), is it a function?

Back

No, because the input 2 has two different outputs (3 and 4).

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What is the definition of a domain in a function?

Back

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?

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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Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

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What is an example of a function?

Back

An example of a function is f(x) = x + 2, where each input x has a unique output.

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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 {(1, 2), (1, 3), (2, 4)}, where the input 1 has two outputs (2 and 3).