Question

a function FX is described by the ordered pairs X Y if if the given function is translated 2 units to the right and then reflected across the x axis what are the ordered pairs that describe the transformed function

Answer 1

The translation of a function n units towards the right will follow the rule:

`\left \{ {{ x_(1) = x - n} \atop {y_(1) = y}} \right.`

A reflection over the x-axis will follow the rule:

`\left \{ {{x_(2) = x } \atop { y_(2) = - y}} \right.`

Applying the two rules at the same time, we have:

`\left \{ {{x' = x - n} \atop {y' = - y}} \right.`

Therefore, in your case:
x' = X - 2
y' = - Y