
vertical line test
$\displaystyle x^4  9x^2  y^4 + 9y^2 = 12$
a) Can this curve be represented by a function as y = f(x)?? explain your answer. > I know that the answer to this is NO because it doesnt pass the vertical line test so cant be expressed as y=f(x)
b) Can this curve be represented by a function as x = g(y)?? explain your answer. > i'm not quite sure what to do about this one.. is the answer to this no also as it doesnt pass the horizontal line test??
help please

You are correct, it can not be expressed as a function of $\displaystyle y$ because it does not pass the horizontal line test.
Another way of stating that would be to say that the curve can not be represented by a function $\displaystyle x = g(y)$ because the inverse of the function does not exist because it does not pass the vertical line test.