Determine if 4x^2 + y^2 = 7 represents y as a function of x

Question

I have to show work.

Determine if 4x^2 + y^2 = 7 represents y as a function of x

Answer 1

the equation graphically is an ellipse. It is not a function, as it doesn't meet the "vertical line" test

functions have only one y value for a given x value. Ellipses have 2 y values for each x value, except for the left and right max and min x coordinates.

divide both sides by 7 to get

4x^2/7 + y^2/7 = 1

x^2/(7/4) + y^2/7 = 1

x^2/(sqr(7/4))^2 + y^2/(sqr7)^2 = 1 is the equation in standard ellipse form

x2/a^2 + y^2/b^2 = 1 where a=sqr(7/4) and b =sqr7