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Consider the table that includes the input and output values of a function. Which answer classifies the function using finite differences? The function is quadratic with a constant second difference of –96. The function is quadratic with a constant second difference of 96. The function is cubic with a constant third difference of –96. The function is cubic with a constant third difference of 96.

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Answer:

b, quadratic with constant second difference of 96

Step-by-step explanation:

ashishdwivedilVT

The function is cubic with a constant third difference of 96.

What is Function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Using differences:

X            f(x)             first difference          second difference             third

3            39                        -                                    -                                -

5            187             (187-39)/2= 74                       -                                -

7            551            (551-187)/7-5 = 182     182 - 74/2 = 54                   -

9           1227          (1227-551)/(9-7)=338   338-182/2=78          78-54/2 = 12

11           2311           (2311-1227)/2=542      542-338/2=102       102-78/2 = 12

According to table,

The function is cubic, because the third average change rate is constant of 12.

12>0, so the third difference is >0 then -96 is false.

Thus, the function is cubic with a constant third difference of 96.

Learn more about function from:

https://brainly.com/question/12431044

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