Question

determine whether the equation defines y as a function of x. y^{2}=6 - x^{2} does the equation define y as a function of x? yes no

Explanation:

Step1: Solve for y

Given $y^{2}=6 - x^{2}$, then $y=\pm\sqrt{6 - x^{2}}$.

Step2: Check the function - definition

For a relation to be a function, for each value of $x$ in the domain, there must be exactly one value of $y$. Here, for a non - zero value of $x$ such that $6 - x^{2}\geq0$, there are two values of $y$ (one positive and one negative square root).

Answer:

No