Which table shows input and output values that represent a cubic function?

Option A: Table C

Step-by-step 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

add an image

step-by-step explanation:

you ignore the remainder, therefore the answer is y = x+2

step-by-step explanation:

you have to divide the denominator by the numerator. you can use synthetic division or long division.

[-5] .     1 .     7 .     11

x + 2 + 1/x+5