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# Transformations 1

### Transformations 1

Translations are operations which move graphical functions up, down, left or right. We can describe them using column vectors.

Translations are operations which allow us to change the position of functions on a graph, while maintaining the same shape.

Translations move functions **up, down, left** or **right**.

$f(x) + a$ moves the graph up by $a$ units

This can occur with any function or point on a graph.

$f(x) - a$ moves the graph DOWN by $a$ units

This can also occur with any function or point on a graph.

Let's translate the point (2, 5) by $f(x) - 2$

We know this would affect the $y$ coordinate, as $f(x)-a$ moves the graph **down**.

The point would move down 2 units

Therefore, the new point would move from $(2,5)$ to $(2,3)$, as the y coordinate would now be 2 units less than previously.

Find the coordinate for the point $(-1,3)$ translated by $f(x)+4$

$f(x+ a)$ moves the graph LEFT by $a$ units

This is slightly counter-intuitive, as you may expect positive to move right. However, this translation moves any function or point to the **left**.

$f(x - a)$ moves the graph right by $a$ units

A negative value of $a$ means that we move any function or point to the **right**

Let's translate the point (2, 5) by $f(x-3)$

This time, we know it affects the $x$ coordinate, as $f(x-3)$ moves the graph horizontally. Remember, this moves the graph to the **right**.

The new coordinate would be $(5,5)$

By moving right, the x-coordinate **increases** in size by 3 units. Therefore, the coordinate moves from $(2, 5)$ to $(5,5)$

If the point $(5,-1)$ is translated by $f(x+4)$, what would the new coordinates be?

The effect of the transformation $f(x) + 5$ is to...

We can also combine translations together, where a function can move both vertically and horizontally.

The effect of the transformation$f(x-2) + 3$ is to move the graph...