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# Transformations of functions

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Author: Andrew Watson

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Tutorial

## Transformations of a Sine Graph

A short video exploring the use of sliders in the free graphing software at www.desmos.com. The graph of y=sin(x) is transformed by adjusting the amplitude, period, and mean line. These are concepts we are familiar with from Year 11 Methods and are a good place to start when exploring the idea of transformation.

## Desmos Sine Graph

https://www.desmos.com/calculator/0l99hdedcm

This is the link for the sine graph that was in the video. While Trig graphs are not covered until Chapter 6, they are a useful starting point as we are familiar with these transformations. Graphs with Sliders can also be created on a CAS Ti-nSpire and can be useful to find solutions dynamically in a CAS active exam.

## Starting to formalise the process

http://www.mathsisfun.com/sets/function-transformations.html

Yes indeed, you read that right, Maths is FUN!

This web-page is not a bad starting place as it looks at a familiar parabola y=x2 and the transformations you were first introduced to in Year 10. Read through the examples and have a 'play' with the graphs by following the links.

There are then 9 questions at the bottom of the page you MUST attempt. Note that our language will be slightly different, but this is an excellent page to start exploring the topic.

## Transformations of a Square Root

Moving on from Maths is fun, this paper is slightly more grown-up (no pretty colours and fonts here) but contains excellent examples and sample questions. Why do you think a square root graph is an excellent choice of graph when starting to development your understanding of transformations?

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## Interactive Square Root Graph

https://www.desmos.com/calculator/vwgbfxr4ic

Practice the transformations of a square root graph from the previous document. Pay particular attention to the domain and range of the new function. Why is the domain restricted in a square root graph? What are the resulting restrictions in the y-values?

## Summary of Transformations

Extract from the study design, and the formal language you can expect to encounter in the end of year exams. This handout should be copied (not cut and pasted) into your summary books.

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