@gkokovidis 

If you can and  have time, make me an example for a function. I did it for $x^2$ while $0<x<2$ to reflect it about $y$-axis but the codes didn't make me that miror part. If I let $x^2$ to be on $-2<x<2$ then refelaction about [[0,1],[0,0]] would coincide on the original function and this makes me sad. Thanks

@Carl Love : Yes, I wan just know that using that functions is useful. Have I been on a right path? Thanks.

Thanks so much for your time.

Thanks so much for your time.