# How do you translate a graph up or down?

Sep 22, 2014

You can translate any function, $y = f \left(x\right)$ using:

$y = f \left(x - h\right) + k$ or
$y - k = f \left(x - h\right)$

If $h$ is positive, the graph will translate to the right.
If $h$ is negative, the graph will translate to the left.
If $k$ is positive, the graph will translate up.
If $k$ is negative, the graph will translate down.

Here is an example:

$f \left(x\right) = {x}^{2} + 2 x$

If we want to translate this up 4 units, then we have:

$y = f \left(x\right) + 4$
$y = {x}^{2} + 2 x + 4$

If we have a different example:

$f \left(x\right) = \frac{1}{x}$
$y = f \left(x\right) + 4$
$y = \frac{1}{x} + 4$

It still works!