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Determining if an Equation Defines a Function

Example

Example: Determining if the Equation $y = x^2 - 7$ Defines a Function

Consider the equation $y = x^2 - 7$ with $x$ as the independent variable. The equation is already solved for $y$ . For any value substituted for $x$ , squaring that value and subtracting $7$ produces exactly one corresponding value for $y$ . Because every input $x$ maps to exactly one output $y$ , the equation $y = x^2 - 7$ defines a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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