- A transformation is simply a change of some sort
**Reflections**(using either the x-axis or y-axis as a mirror line)**Translations**(moving the whole graph in the x and/or y direction)

- You should be able to recognise these two different sorts of transformation and apply them to a given graph.

Given a transformation in function notation, then

**y = f(x + a),**represents a**−a**units in the**x**axis**a**is inside the bracket- Note the change of sign highlighted!

**y = f(x) + b,**represents**+ b**units in the**y**direction**a**is outside the bracket

- For example,
**y = f(x + 3) + 2**means- a translation of y = f(x) by
**−3**in**x**the direction and**+2**in the**y** - Note the change of sign in the
*x*direction as pointed out above!

- a translation of y = f(x) by

- Some questions give a transformed function in the form
**y = f(x + a)**or**y = f(x) + a**and ask you to**describe the transformation** - To
**describe**a translation**fully**, you must include;- the transformation:
**"translation"** - the
**direction**in the**x-axis****and**in the**y-axis**- this can be given as a worded description, e.g. "3 left and 2 up" / "−3 in the x-axis and +2 in the y-axis"
- or it can be given as a
**vector ,**e.g. "by "

- the transformation:
- Remember that
- if the
**a**is**inside**the bracket, its a translation by**−a**in the**x-axis** - if the
**a**is**outside**the bracket, its a translation by**a**in the**y-axis**

- if the

- y = f(x + a); "a"
**next to**x, translates in**x-axis**by**−a** - y = f(x) + a; "a"
**not**next to x, translates in**y-axis**

The graph of is shown on the graph below.

On the same graph sketch .

This is a translation by −3 in the x direction (i.e. 3 to the left, note the change of sign again) and +2 in the y direction (i.e. 2 up)

So we copy the given graph in its new position. Translate key points- endpoints and vertices like the vertex shown below- first, then join the points with straight lines

Describe the transformation that maps the graph of to the graph of .

The number inside the bracket (next to x) is −4 so this is a translation by +4 in the x-axis (note the change in sign again)

The number outside the bracket (not next to x!) is −6 so this is a translation by −6 in the y-axis

**Translation by **or

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