# What does it mean to translate a graph?

Jun 12, 2015

Translations are simply horizontal and/or vertical shifts. So, $y = \sqrt{x} - 2$ is shifted 2 units down from $y = \sqrt{x}$, while $y = \sqrt{x - 2}$ is shifted 2 units right of $y = \sqrt{x}$.

$y = \sqrt{x}$:
graph{sqrtx [-10, 10, -5, 5]}

$y = \sqrt{x} - 2$:
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]}