1Cademy - Example: Determining if the Equation $$x + y^2 = 4$$ Defines a Function

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Determining if an Equation Defines a Function

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Example: Determining if the Equation $x + y^2 = 4$ Defines a Function

Consider the equation $x + y^2 = 4$ where $x$ is the independent variable. Isolate the $y$ term by subtracting $x$ from both sides to obtain $y^2 = -x + 4$ . Supplying a test value such as $x = 0$ gives $y^2 = 4$ . This yields two distinct values for $y$ : $2$ and $-2$ . Since a single $x$ maps to multiple values of $y$ , the equation $x + y^2 = 4$ does not define a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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