How do I find the formula here?

Question

There are a row of digits 6 4 2 0 0 2 4 6 . There are also correspondig numbers to each of them: 1 2 3 4 5 6 7 8

How do we find which formula to use, in order to get the digits, knowing their number?

For example for the first four digits it could be possible to use y=8-2n. But we need a formula where we would get 0 both from 4 and 5...

Answer 1

Notice that

$$6 \ 4 \ 2 \ 0 \ 0 \ 2 \ 4 \ 6$$ is symmetric in nature.

1. What type of function would absolutely (hint hint) allow you to convert $$1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8$$ to a symmetric row of numbers first?

   The absolute function: $|x|$

2. What is the number (not necessarily integer) right in the middle of the input row?

   The median: $4.5$

3. What functions convert real numbers to an integer nearby?

   The floor and ceiling functions

Spoiler:

$$y=2\times\left\lfloor|x-4.5|\right\rfloor$$