Determine whether the equation defines y as a function of x.
-$$x y + 9 y = 1$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question

Quizplus · Accepted Answer

To determine if $y$ is a function of $x$, we need to see if for each $x$, there is exactly one $y$. We can solve the equation for $y$ in terms of $x$: $xy + 9y = 1 \Rightarrow y(x + 9) = 1 \Rightarrow y = \frac{1}{x + 9}$. This equation defines $y$ as a function of $x$ because for each $x$, there is exactly one $y$, except when $x = -9$ (which would make the denominator zero, but this is a restriction, not a violation of the function definition).

Determine Whether the Equation Defines Y as a Function of X