Rewrite function if moved by a vector and is mirrored

[JG FRANKO]

1. There is a function f(x). Write regulations for it if: -you move it by a vector r=(a,b),
-you mirror it over x or y axis.2. f(x) isn't exactly given. Vector is r(a,b).3. If we move it by vector: f(x-a)+b,
If we mirror it over x: -f(x)
If we mirror it over y: f(-x)
So if I am correct, let's say we have f(x)=x^2+x-4, then when we move it for the vector: f(x)=x^(2-a)+x+(-4+b).
If we mirror it over x: f(x)=(-x)^2-x-4 and if we mirror it over y : f(x)=-(x^2)-x+4

Is this correct?

graphs of f(x) that I got for mirroring: https://www.wolframalpha.com/input/?i=f(x)=(-x)^2-x-4
https://www.wolframalpha.com/input/?i=f(x)=-(x^2)-x+4

 

[Ssnow]

If we mirror it over x: f(x)=(-x)^2-x-4 and if we mirror it over y : f(x)=-(x^2)-x+4

I think the opposite mirror it over $x$: $f(x)=-(x^2)-x+4$ and if we mirror it over $y$ : $f(x)=(-x)^2-x-4$