Answer
Yes
Work Step by Step
Let us solve for $y$.
$-2y=5-3x^2$
$y=\frac{5-3x^2}{-2}$
$y$ is uniquely defined for all $x$, so the given equation defines $y$ as a function of $x$. So the equation defines a function.

You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.