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Year 11 - Maths

Transforming graphs: combinations of transformations

Transformations of graphs

Unit Summary

In this unit pupils learn how to perform transformations on functions both algebraically and visually.

Lesson Summary

You will learn to recognise the effect of applying a combination of transformations to a function.

Key Notes

Desmos is an effective tool for showing the effects of this transformation
The actual function itself does not need to be known
The order of transformations is defined by the priority of operations

Vocabulary To Learn

Transformation: A transformation is a process that may change the size, orientation or position of a shape or graph.

Common Mistakes To Avoid

For the combined transformation $$3$$f$$(x-2)$$ order does not matter so pupils may assume that order never matters.

3 Quick Questions (With Answers)

1. Solve this in steps: explain the method from this lesson and why each step matters.

Desmos is an effective tool for showing the effects of this transformation. The actual function itself does not need to be known.

2. Use this key word in a maths sentence and explain it clearly. 'Transformation'

A transformation is a process that may change the size, orientation or position of a shape or graph. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: For the combined transformation $$3$$f$$(x-2)$$ order does not matter so pupils may assume that order never matters. Correction: For $$3$$f$$(x-2)$$ the $$3$$ affects the output, the $$y$$ value, and the $$-2$$ affects the input, the $$x$$ value. Model to show that these can happen in either order. Then point out that $$3$$f$$(x)-2$$ is two effects on the output.

More Lessons In This Unit

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