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**Graph translations** involve shifting the graph of a function either horizontally or vertically without altering its shape. The translation changes the position of the graph on the coordinate plane, but the basic form of the graph remains unchanged.

A vertical translation shifts the graph up or down. The function:

\[y = f(x) + k\]

moves the graph of \(y = f(x)\) **k units up** if \(k > 0\), and **k units down** if \(k < 0\).

A horizontal translation shifts the graph left or right. The function:

\[y = f(x + h)\]

moves the graph of \(y = f(x)\) **h units** to the **right** if \(h < 0\), and **h units** to the **left** if \(h > 0\).

You can combine horizontal and vertical translations. The function:

\[y = f(x + h) + k\]

translates the graph of \(y = f(x)\) by **h units horizontally** and **k units vertically**.

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