Given the sequence 2, 4, 6, 8, ... where x = 0, 1, 2 ...,

what is the function rule?

f (x) = 2x + 2

f (x) = 2

f (x) = 2x

f (x) = 2x - 1

The function rule for the given sequence is f (x) = 2x + 2.

Step-by-step explanation:

A function is a relation which implies that for every input, there will be one output. i. e. for every value of x, there is only one value for y. The function rule describes how to convert an input value (x) into an output value (y) for a given function.

In the given function,

f (x) = 2x + 2, where x = 0, 1, 2 ...,

substituting x = 0, we get

f (x) = 2 (0) + 2 = 2

substituting x = 1, we get

f (x) = 2 (1) + 2 = 4

substituting x = 2, we get

f (x) = 2 (2) + 2 = 6

and it goes on like 2, 4, 6, 8, ...

This satisfies the function f (x) = 2x + 2.