# Translating graphs

The translation of graphs is explored

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

## Functions

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.

## Translations parallel to the y-axis

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.

### Example 1 Draw the graphs of and .

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

### Example 2 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 .

## Translations parallel to the x-axis

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.

### Example 1 Draw the graphs of and .

### Example 2 Draw the graphs of and . represents a translation of the graph of by the vector .