Year 11 - Maths
Transforming graphs: y = af(x)
Transformations of graphs
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
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 the transformation y = af(x) to a graph.
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 graph is stretched by a scale factor of a in the y-direction
Vocabulary To Learn
- Transformation: A transformation is a process that may change the size, orientation or position of a shape.
Common Mistakes To Avoid
- Pupils confuse 'stretch' transformations. Many transformations of the form $$y=a$$f$$(x)$$ have the appearance of a compression towards the $$y$$-axis rather than a 'stretch' in the $$y$$-direction.
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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils confuse 'stretch' transformations. Many transformations of the form $$y=a$$f$$(x)$$ have the appearance of a compression towards the $$y$$-axis rather than a 'stretch' in the $$y$$-direction. Correction: Interpreting the notation is key. $$y=a$$f$$(x)$$ is the output of f$$(x)$$ being multiplied by $$a$$. Which coordinate is the output? The $$y$$ coordinates change by a scale factor of $$a$$ so this must be a stretch in the $$y$$-direction.
More Lessons In This Unit
- Checking and securing understanding of function notation Study Guide
- Checking and securing understanding of moving between function notation and the definition Study Guide
- Problem solving with graph transformations Study Guide
- Transforming graphs: combinations of transformations Study Guide
- Transforming graphs: y = −f(x) Study Guide
- Transforming graphs: y = f(−x) Study Guide
- Transforming graphs: y = f(ax) Study Guide
- Transforming graphs: y = f(x + a) Study Guide
- Transforming graphs: y = f(x) + a Study Guide
Browse all guides in the Year 11 Maths guide library.