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

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Determining if an Equation Defines a Function

Example

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

Consider the equation $x + y^2 = 1$ with $x$ as the independent variable. Isolating the $y$ term by subtracting $x$ yields $y^2 = -x + 1$ . If a value such as $x = 0$ is substituted, the equation becomes $y^2 = 1$ . This results in two possible solutions for $y$ : $1$ and $-1$ . Because substituting a single value for $x$ produces more than one corresponding value for $y$ , the equation $x + y^2 = 1$ does not define a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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