3.1 Definition of a Function

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What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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What is the vertical line test?

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The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

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What does it mean for a mapping diagram to represent a function?

Back

A mapping diagram represents a function if each input (domain) is connected to exactly one output (range).

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What is the definition of 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.

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What is the definition of the range of 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.

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How can you determine if a table of values represents a function?

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A table of values represents a function if no two different inputs (x-values) correspond to the same output (y-value).

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What is an example of a function?

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An example of a function is f(x) = 2x + 3, 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 the set of points {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

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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 related to exactly one input, meaning no two different inputs produce the same output.

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.