Question

What does it mean to translate a graph?

Answer 1

Translations are simply horizontal and/or vertical shifts. So, `y = sqrtx - 2` is shifted 2 units down from `y = sqrtx`, while `y = sqrt(x-2)` is shifted 2 units right of `y = sqrtx`.

`y = sqrtx`:
graph{sqrtx [-10, 10, -5, 5]}

`y = sqrtx - 2`:
graph{sqrtx - 2 [-10, 10, -5, 5]}

`y = sqrt(x - 2)`:
graph{sqrt(x-2) [-10, 10, -5, 5]}

`y = sqrt(x - 2) - 2`:
graph{sqrt(x-2) - 2 [-10, 10, -5, 5]}