A **translation** is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

The graph of where is the same as the graph of .
Writing equations as **functions** in the form is useful when applying translations and reflections to graphs.

If , then . Here we are adding to the whole function.

The addition of the value represents a vertical translation in the graph. If is positive, the graph translates upwards. If is negative, the graph translates downwards.

Draw the graphs of and .

This is a translation of by 3 units in the **positive** direction.

Draw the graphs of and .

This is a translation of by 2 units in the **negative** direction.

represents a translation of the graph of by the vector .

If then

Here we add to , not to the whole function. This time we will get a horizontal translation. If is positive then the graph will translate to the left. If the value of is negative, then the graph will translate to the right.

Draw the graphs of and .

Draw the graphs of and .

represents a translation of the graph of by the vector .