# Transformations of Functions

- Created by: Danny Hillman
- Created on: 15-05-11 20:38

**Transformations of Functions**

**A transformation of a function is a way of mapping that function to another. **

**The most commonly asked question in an exam on this topic is: Which geometrical transformation maps the graph y = f(x) to y = g(x)? **

**There are three types of transformation: translations, stretches and reflections. This revision sheet will take you through all three in a step-by-step manner, including some exam tips for how to obtain full marks on any transformation question.**

**An important element to remember when doing any form of transformation is **

**Vertical**

**Outside**

**Normal**

**Horizontal**

**Inside**

**Reversed**

**Translations**

**A translation is a type of transformation which moves a function from one position to another. These are always written in vector form and are recognised through the process of addition/subtraction.**

**y = x^2 maps to y = (x^2) + 2**

**Here, the geometrical transformation would be described as a:**

**Translation 0**

** 2 where the 0 and 2 are enclosed in a single bracket. **

**This is because, according to VON HIR, the action we are doing to the function of x (x^2 in this case) is outside of the function we began with, meaning it is a vertical translation (in the y-direction) and is taken as it is. **

**If we mapped y = x^2 to y = (x+2)^2**

**the transformation would then become:**

**Translation -2**

** 0**

**VON HIR dictates that anything INSIDE the function we began with is in the x-direction (horizontal) and becomes reversed (i.e. positive becomes negative) **

**y = x^2 maps to y = ((x+2)^2) + 2 would be described as a:**

**Translation -2**

** 2**

**To generalise: if y = f(x) maps to y = f(x-a) + b**

**the geometrical transformation used to describe it would be a**

**Translation a**

** **…

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