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To determine which function passes through all the points in the table, we can create equations using the given points and then check which function satisfies all the equations.
From the table:
(0, 0) gives us: y = 0
(1, 1) gives us: y = 1
(-1, -1) gives us: y = -1
(2, 2) gives us: y = 8
(3, 3) gives us: y = 27
Looking at the given function choices:
A. y = -x does not satisfy the points (2, 8) and (3, 27).
B. y = -x^2 does not satisfy the points (1, 1) and (2, 8).
C. y = -x^3 does not satisfy the points (0, 0) and (1, 1).
D. y = x^2 satisfies all the given points.
E. y = x^3 does not satisfy the points (1, 1) and (2, 8).
Therefore, the correct function that passes through all the given points in the table is y = x^2.