Year 11 - Maths
Transforming graphs: y = f(x + a)
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 = f(x + a) 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 transformed by a horizontal translation in the opposite direction
Vocabulary To Learn
- Function: A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
- Transformation: A transformation is a process that may change the size, orientation or position of a shape or graph.
Common Mistakes To Avoid
- f$$(x)+5$$ is a translation of $$+5$$ in the $$y$$-direction so pupils may assume that f$$(x+5)$$ is a translation of $$+5$$ in the $$x$$-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. 'Function'
A function is a mathematical relationship that uniquely maps values of one set to the values of another set. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: f$$(x)+5$$ is a translation of $$+5$$ in the $$y$$-direction so pupils may assume that f$$(x+5)$$ is a translation of $$+5$$ in the $$x$$-direction. Correction: Visually showing pupils, using graphing technology, that f$$(x+5)$$ is not a translation to the right will help. Showing them a comparison of the two tables of values for both functions shows them why this happens.
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 = af(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
Browse all guides in the Year 11 Maths guide library.