Translations are changes we make to function graphs, moving them around on the grid. We can shift these graphs sideways or up and down.

Horizontal Translations:

• When we move a graph to the right, we write it as $f(x - h)$. Here, $h$ tells us how far to the right we go.
• If we move the graph to the left, we write it as $f(x + h)$.

Vertical Translations:

• To shift a graph up, we use $f(x) + k$, where $k$ shows how far up we move.
• To shift a graph down, we write $f(x) - k$.

How This Affects Graphs:

• Moving the graph sideways (horizontal translations) does not change its shape. It only changes the x-values.
• Moving the graph up or down (vertical translations) changes the y-values. The shape stays the same, but the position of the graph changes.