Answer
y is a function of x
Work Step by Step
The equation $x^2 y-x^2 +4y=0$ can be rewritten as follows:
$x^2 y-x^2 +4y=0$
$x^2 y +4y=x^2$
$y(x^2 +4)=x^2$
$y=\frac{x^2}{x^2 +4}$
Since each x value will only yield one y value, the equation $y=\frac{x^2}{x^2 +4}$ and its equivalent $x^2 y-x^2 +4y=0$ are both functions.
Also the graph shows that the equation passes the vertical line test, so it is a function.
