# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-functions-Function-Transformations.html


## Function Transformations

"Not a lot of people know this, but I'm very good at mathematics. When I was an angry teenager, I used to sit in my room and do quadratic equations to calm myself down " Samantha Bond


#### Translations


##### What you have to know:

- Understand basic functions such as \(y=x^2\), \(y=x^3\), \(y=\sqrt{x}\), \(y=|x|\), and \(y=\frac1x\).
- Be able to plot simple functions using a GDC.

##### Key Points

- 1. Watch the video:
- A translation moves a graph without changing its shape.

#### Reflections


##### What you have to know:

- Recognise the effect of negative signs inside and outside a function.

##### Key Points

- 1. Watch the video:

#### Stretches and Compressions


##### What you have to know:

- Understand the difference between horizontal and vertical transformations.

##### Key Points

- 1. Watch the video:

#### Combined Transformations


##### What you have to know:

- Be confident with individual transformations before combining them.

##### Key Points

- 1. Watch the video:

#### Extra


##### Material and references:

- Hodder Mathematics AA SL: Functions and Transformations Chapter

##### Key Points

- 1. A translation by \(a\) units horizontally and \(b\) units vertically: \[ y=f(x-a)+b \]
- 2. Reflection in the \(x\)-axis: \[ y=-f(x) \]
- 3. Reflection in the \(y\)-axis: \[ y=f(-x) \]
- 4. Vertical stretch by factor \(k\): \[ y=kf(x) \]
- 5. Horizontal stretch by factor \(k\): \[ y=f\left(\frac{x}{k}\right) \]
- 6. Remember: transformations inside the bracket affect the graph horizontally, while transformations outside the bracket affect the graph vertically.
- 7. The order of transformations matters when several transformations are combined.

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