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

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.  

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