1Cademy - Example: Determining if the Equation $$x + y^2 = 3$$ Defines a Function

Learn Before

Determining if an Equation Defines a Function

Example

Example: Determining if the Equation $x + y^2 = 3$ Defines a Function

Consider the equation $x + y^2 = 3$ where $x$ is the independent variable. First, isolate the $y$ term by subtracting $x$ from both sides to get $y^2 = -x + 3$ . Substitute a value for $x$ , such as $x = 2$ , which yields $y^2 = -2 + 3$ , simplifying to $y^2 = 1$ . This implies that $y$ can be $1$ or $-1$ . Because a single value of $x$ corresponds to more than one value of $y$ , the equation $x + y^2 = 3$ does not define a function.

Updated 2026-05-06

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related