Answer:
Option A: Table C
Explanation:
A cubic function has the following structure:
f(x) = ax3 + bx2 + cx + d
To check if the table values represent a cubic function, we can use the pairs (x, f(x)) to find the values of a, b, c and d.
For table A, we have:
pair (0,64): d = 64
pair (-4,76): -64a + 16b - 4c = 12
pair (-8,88): -512a + 64b - 8c = 24
pair (4,52): 64a + 16b + 4c = -12
solving this system, we have a=0, b=0, c=-3 and d=64
As a=0, this is not a cubic function.
For table B, we have:
pair (0,0): 0 = d
pair (-4,24): -64a + 16b - 4c = 24
pair (-8,80): -512a + 64b - 8c = 80
pair (4,8): 64a + 16b + 4c = 8
solving this system, we have a=0, b=1, c=-2 and d=0
As a=0, this is not a cubic function.
For table C, we have:
pair (0,64): d = 64
pair (-4,128): -64a + 16b - 4c = 64
pair (-8,576): -512a + 64b - 8c = 512
pair (4,0): 64a + 16b + 4c = -64
solving this system, we have a=-1, b=0, c=0 and d=64
As a is not 0, this is a cubic function.
For table D, we have:
pair (0,64): 0 = d = 64
pair (-4,80): -64a + 16b - 4c = 16
pair (-8,128): -512a + 64b - 8c = 64
pair (4,80): 64a + 16b + 4c = 16
solving this system, we have a=0, b=1, c=0 and d=64
As a=0, this is not a cubic function.
So the correct option is A: Table C