The translation of a function n units towards the right will follow the rule:
[tex] \left \{ {{ x_{1} = x - n} \atop {y_{1} = y}} \right. [/tex]
A reflection over the x-axis will follow the rule:
[tex] \left \{ {{x_{2} = x } \atop { y_{2} = - y}} \right. [/tex]
Applying the two rules at the same time, we have:
[tex] \left \{ {{x' = x - n} \atop {y' = - y}} \right. [/tex]
Therefore, in your case:
x' = X - 2
y' = - Y
