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Determining if an Equation Defines a Function

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

Consider the equation $y - x^2 = 2$ where $x$ is the independent variable. Solve for $y$ by adding $x^2$ to both sides, which gives $y = x^2 + 2$ . For any real number substituted for $x$ , squaring it and adding $2$ yields exactly one corresponding value for $y$ . Because each value of $x$ produces only one unique value of $y$ , the equation $y - x^2 = 2$ defines a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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