What is a function?

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What is a function?

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A function is a relation where every input (x-value) is associated with 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 used 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.

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What is a relation in mathematics?

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

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Can a function have the same output for different inputs?

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Yes, a function can have the same output for different inputs, but each input must have only one output.

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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 gives a unique output.

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What is an example of a non-function?

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An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 has two different outputs.

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What does it mean for a function to be one-to-one?

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

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What is an exponential function?

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An exponential function is a function in which an independent variable appears in the exponent, typically in the form f(x) = a * b^x.

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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.