Question

is x^2+4y^2=1 a function?

Answer 1

Solve for y first:

\[\large x^2+4y^2=1\]

\[\large 4y^2=1-x^2\]

\[\large y^2=\frac{1-x^2}{4}\]

\[\large y=\pm\sqrt{\frac{1-x^2}{4}}\]

So this means that

\[\large y=\sqrt{\frac{1-x^2}{4}} \ \ \text{or} \ \ y=-\sqrt{\frac{1-x^2}{4}}\]


But y can't be two different values for any given x value. So this is NOT a function.

Answer 2

No because you have a y^2 term. Any equation with y^2 is not a function.

Answer 3

that's one good way to remember it

Answer 4

y^2 can be a function; .... its just that this equation is a circle, and therefore not a funtion