Answer:
(x, y) ⇒ (x +1, y)
Explanation:
The work you show is correct. The translation vector is added to the original coordinates. That sum is the translation rule.
Translation Vector
Each point of the image is 1 unit to the right of its pre-image position. This means the translation vector is v = <1, 0>.
Transformation Rule
The rule you're looking for adds this vector to the (x, y) coordinates:
(x, y) ⇒ (x +1, y)