Functions

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What is a function?

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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 definition of the domain of a function?

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The domain of a function is the complete set of possible values of the independent variable (input) 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 complete set of possible values of the dependent variable (output) that results from using the function.

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How can you determine if a graph represents a function?

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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 for y to be a function of x?

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It means that for every value of x, there is exactly one corresponding value of y.

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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 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 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.

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What is a quadratic function?

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A quadratic function is a function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.