Answer
The equation does not define $y$ as a function of $x$.
Work Step by Step
An equation defines $y$ as a function of $x$ if for every value of $x$, the equation gives only one corresponding value of $y$.
Solve for $y$ in the given equation to obtain:
$x^2-4y^2=1
\\-4y^2=1-x^2
\\y^2=\dfrac{1-x^2}{-4}
\\\sqrt{y^2} = \pm \sqrt{\dfrac{1-x^2}{-4}}
\\y= \pm \sqrt{\dfrac{1-x^2}{-4}}$
The equation gives two different values of $y$ for most values of $x$.
Thus, the equation does not define $y$ as a function of $x$.