Graph Transformations 6
In the Activity below we combine all the graph transformations we have met into one.
We have the graph of y = f(x) and y = cf(dx + a) + b and y = cf(d(x + a)) + b where a = 0, b = 0, c = 1 and d = 1 to start with.
Use the pen tool to sketch each of the following graphs using the transformations we have seen.
You may need to drag the screen around to see enough information.
1) y = f(x  3) + 2

2) y = f(2x  2)

3) y = 2f(3x)

4) y = 3f(x + 4)

5) y = f(2x + 3)

6) y = 0.5f(x + 2) + 2

Ideas for Teachers
This Activity will really test whether the students have got a good grasp of the ideas of Graph Transformations. Get them to work in pairs maybe, to scribble on their activities what they think the transformed graph will look like. Or, give them printed axes to sketch on if you are showing them the activity on the board. Either way, it is important they predict first, before you ask one of them up to the board to scribble on what they think will happen in each case. Then check their prediction using the constant controllers. The functions given are a guide only, and you will need to come up with suitable functions for your class.
This Activity will really test whether the students have got a good grasp of the ideas of Graph Transformations. Get them to work in pairs maybe, to scribble on their activities what they think the transformed graph will look like. Or, give them printed axes to sketch on if you are showing them the activity on the board. Either way, it is important they predict first, before you ask one of them up to the board to scribble on what they think will happen in each case. Then check their prediction using the constant controllers. The functions given are a guide only, and you will need to come up with suitable functions for your class.
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