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Determining if an Equation Defines a Function

Example

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

Consider the equation $y = x^2 + 1$ where $x$ is the independent variable. The equation is already solved for $y$ . For any value substituted for $x$ , squaring it and adding $1$ results in exactly one corresponding value for $y$ . For example, if $x = 2$ , then $y = (2)^2 + 1$ , which simplifies to $5$ . Since each value of $x$ produces only one unique value of $y$ , the equation $y = x^2 + 1$ defines a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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