y =√16 − x² determine whether the equation represents y as a function of x:

Question

y =√16 − x²

determine whether the equation represents y as a function of x:

Answer 1

y = sqr(16-x^2) is the top half of a circle with radius 4 and center = origin

y^2 = 16 -x^2

x^2 + y^2 = 4^2

It's a function. It passes the vertical line test

sqr16-x^2) is the positive square root only

if it were f(x) = y = + sqr(16-x^2) it would be a full circle and not a function.