Transforming Functions - The Stretch


'Explore a transformation to help Mr Greedy slim down his tummy'

Mr Greedy liked to eat! In fact Mr Greedy loved to eat, and the more he ate the fatter he became.[1]

However, as you can see Mr Clever has found a way to slim Mr Greedy down which I thinks suits him a lot better. Can you work out what mathematical transformation that Mr Clever has used to slim down Mr Greedy's tummy?

Aim

The aim of this activity is for students to discover what effect stretching graphs has on their equations. We will look at transforming shapes and what happens to the coordinates of the shapes under this transformation. Once this is understood the same transformation will be applied to functions. Geogebra will be used to visualise the transformations and provide a medium for students to experiment with their own ideas. The activity includes applets to help teachers clarify understanding. The final task is a game to check what has be learnt. Watch the following video (no sound) to get a complete overview of the activity:

Resources & Description

The following gives an overview of the activity and all the resources included in this page that could be used. All the resources follow in the order that they are given here.

  1. Students are asked to compare 2 different transformations. This could be led by the teacher or individually.
     
  2. To understand how to create stretches in Geogebra students could watch this video individually. Alternatively the teacher could show the video to the whole class.

  3. Here is an activity that can be completed on paper (but using Geogebra to help ). It will help students understand the effect stretches have on coordinates. This is a key part of the activity to set up transforming functions.

  4. A second help video is included to show how to stretch functions using Geogebra. A third video will give assistance in entering trigonometric functions in Geogbra is also included.

  5. Here students are led through an investigation to discover the effect a stretch from the y and the x axis has on the equation. Students are encouraged to test out their ideas using Geogebra.

  6. There is a plenary that the teacher could to use to focus and bring together the understanding of the horizontal and vertical stretches.

  7. Finally, a guess the function game is included for students to check their understanding. Horizontal and vertical stretches are applied to the sine function. Students must enter the correct equation to match-up the graphs.

  8. Some suggestions of further activiities are included for extension work!

 1. Describe the transformation

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 2. Geogebra-Stretching Shapes

Watch this video to see how you can stretch shapes in Geogebra:

 3. Stretching Shapes

This part will help students understand the effect stretches have on coordinates. Click on the image below to download the WORD document. This can be printed out or completed digitally.

 4. Geogebra-Stretching Functions

Watch this video to get help with stretching functions in Geogebra:

Entering trigonometric functions in Geogebra can be tricky. See how to do it with this video:

 5. Stretching Functions

Here students are led through an investigation to discover the effect a stretch from the y or the x axis has on the equation. Students are encouraged to test out their ideas using Geogebra. Click on the image below to download the WORD document. This can be printed out or completed digitally.

 6. Plenary

The teacher may wish to use these two applets to focus and bring together the understanding of the horizonatal and vertical stretches. Use the slider to change the scale factor of the stretch and challenge the students to give the equation of the new graph.

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 7. The Stretch Game

Make the dotted blue curve lie on top of the gold curve by entering the correct values in the boxes. Press refresh for a new question.

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 8. Extension

For another activity looking at stretching and translating exponential functions try:

Exponential Functions

This activity will challenge high achieving students to learn about the properties of exponential functions and their transformations. Interactive applets and quizzes get the students to discover the properties for themselves then there are a couple of games to challenge them to 'copy the function'. Watch the short video below for a quick overview.

For another activity looking at stretching and translating trig functions try:

Trigonometric Function Family

This activity gets students to produce families of trigonometric functions (like the one on the right) using dynamic geometry software. By exploring the effect of changing parameters they really get a deep understanding of the properties of the main transformations: translations and stretches. Get ready for "Oos and Ahhs"!


Footnotes

  • 1. Source: Mr Greedy by Roger Hargreaves
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