Review Identify Functions

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What is a function in mathematical terms?

Back

A function is a relation where every input has exactly one output.

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How can you determine if a relation is a function?

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A relation is a function if no two ordered pairs have the same first element with different second elements.

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What is the vertical line test?

Back

The vertical line test is a method 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.

Front

What does it mean for a graph to be a function?

Back

A graph represents a function if each x-value corresponds to exactly one y-value.

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Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input.

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What is an example of a function?

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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)}, where the input 1 has two different outputs.

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What is the definition of a one-to-one function?

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A one-to-one function is a function where each output is associated with exactly one input.

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What is the definition of a many-to-one function?

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A many-to-one function is a function where multiple inputs can produce the same output.

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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) for the function.