Questions: Determine whether the following equation defines y as a function of x x^2 + y^2 = 144 Does the equation x^2 + y^2 = 144 define y as a function of x?

Solution Steps

To determine if the equation \(f(x, y) = 144\) defines \(y\) as a function of \(x\), we first attempt to rearrange the equation to express \(y\) in terms of \(x\), i.e., \(y = g(x)\).

After rearranging, we need to check if for every value of \(x\), there is exactly one corresponding value of \(y\). This is crucial because the definition of a function requires that each input \(x\) maps to exactly one output \(y\).

It's also important to consider the domain of \(x\), especially if rearranging for \(y\) involves operations that restrict the domain of \(x\). For instance, operations like square roots require non-negative arguments.

Final Answer: