Final answer:
The equation x²+y²=16 does not represent y as a function of x because for most x-values within the interval [-4, 4], there are two possible y-values, which violates the definition of a function where each x-value should map to exactly one y-value.
Step-by-step explanation:
To determine whether the equation x²+y²=16 represents y as a function of x, we look at the relation described by the equation. This equation represents a circle with a radius of 4, centered at the origin (0,0) on a Cartesian plane. For each x-value within the interval [-4, 4], there are two possible y-values: one positive and one negative, except at x=-4 and x=4 where y is 0. Because there are two different y-values for most x-values, y is not a function of x according to the definition of a function, which states that each x-value should map to exactly one y-value