Determine whether or not the equation defines y as a function of x.

Question

y² = 7-x².

function.

not a function.

Answer 1

Not a function

y^2 = 7 - x^2 is equivalent to x^2 + y^2 = 7 which is a circle with center at the origin and radius = sqr7

a circle is not a function. It fails the vertical line test. A vertical line can cut the circle in more than one place. there are two values for each x value in the circle (except the left and right extremities).

for x=0, y = either sqr7 or -sqr7

points (0, sqr7) and (0, -sqr7) are both points on the circle. That makes it Not a function.