Identifying and Describing Functions

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What is a function?

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A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

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How can you determine if a graph represents a function?

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You can use the Vertical Line Test: if a vertical line intersects the graph at more than one point, then the graph is not a function.

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What is the definition of a relation?

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A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

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

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

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What is the Vertical Line Test?

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

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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 for every x-value, there is 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 equation x^2 + y^2 = 1, which gives two y-values for some x-values.

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What is a one-to-one function?

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A one-to-one function is a function where each output is paired with exactly one input, meaning no two different inputs produce the same output.

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What is a mapping diagram?

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A mapping diagram visually represents a function by showing how each input is paired with its corresponding 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 which the function is defined.