Question

answer the questions below to determine what kind of function is depicted in the table below.

x	1	2	3	4	5
f(x)	-3	43	181	411	733

answer attempt 1 out of 2
this function is because

Explanation:

Step1: Calculate first - order differences

$43-(-3)=46$, $181 - 43=138$, $411-181 = 230$, $733 - 411=322$

Step2: Calculate second - order differences

$138 - 46=92$, $230-138 = 92$, $322-230=92$

Step3: Analyze the result

Since the second - order differences are constant, the function is a polynomial function of degree 2 or higher. In general, if the $n$th - order differences of a function are constant, the function is a polynomial of degree $n$. Here, the second - order differences are constant, so it is a polynomial function.

Answer:

A polynomial function