Final answer:
Option C, x + y^2 = 16, is not a function because it fails the vertical line test; for certain x-values, there might be more than one possible y-value.
Step-by-step explanation:
To determine which equation is not a function, we need to apply the vertical line test. This test states that if a vertical line intersects the graph of the equation at more than one point, then the equation does not represent a function.
A. y = x^2 - 4 is a function since every x-value has exactly one corresponding y-value.
B. x + 2y = 8 can be rearranged to y = (8 - x)/2, which is also a function.
C. x + y^2 = 16 is not a function because, for a single x-value, there might be two possible y-values (one positive and one negative).
D. y = 3x - 20 is a linear function and thus has a one-to-one relationship between x-values and y-values.
Therefore, option C, x + y^2 = 16, is the equation that is not a function.