Use successive differences to classify the function represented in the table as linear, quadratic, cubic or other. Show all your work. x - 3 - 2 - 1 0 1 2 3 g (x) - 29 - 10 - 3 - 2 - 1 6 25

Answer: The function shows by the table is cubic function.

Explanation: Since, the given values of the function are

f (x) : - 29 - 10 - 3 - 2 - 1 6 25

First difference: 19 7 1 1 7 19

Second difference: - 12 - 6 0 6 12

Third difference: 6 6 6 6

Since, here, the value in third difference is repeating to 6. Therefore, according to the definition of successive difference, equation must have three degree. So, it is a cubic equation.