Question

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

Explanation:

Step1: Solve the equation for y

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

Step2: Check the function - definition

For a relation to be a function, for each input $x$ there must be exactly one output $y$. Here, for a single value of $x$ (e.g., when $x = 6$, $y=\pm2$), there are two possible values of $y$. So, $y$ is not a function of $x$.

Answer:

No