Year 10 - Maths
Key features of a reciprocal graph
Non-linear 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 graphical representations of non-linear graphs are introduced and explored, and their key features identified.
Lesson Summary
You will learn to identify the key features of a reciprocal graph.
Key Notes
- A reciprocal graph has a distinct shape.
- A reciprocal graph has two asymptotes.
- Reciprocal graphs of the form y = k/x have the axes as their asymptotes.
Vocabulary To Learn
- Asymptote: An asymptote is a line that a curve approaches but never touches.
Common Mistakes To Avoid
- All reciprocal graphs appear only in two quadrants and have both axes as asymptotes.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A reciprocal graph has a distinct shape. A reciprocal graph has two asymptotes.
2. Use this key word in a maths sentence and explain it clearly. 'Asymptote'
An asymptote is a line that a curve approaches but never touches. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: All reciprocal graphs appear only in two quadrants and have both axes as asymptotes. Correction: Show pupils the graphs of the $$y={1\over{x}}$$, then $$y={1\over{x}}+1$$, then $$y={1\over{x+1}}$$ and get them to compare which forms have which axes as asymptotes.
More Lessons In This Unit
- Advanced problem solving with non-linear graphs Study Guide
- Checking and securing understanding of drawing quadratic graphs Study Guide
- Drawing cubic graphs Study Guide
- Drawing exponential graphs Study Guide
- Drawing reciprocal graphs Study Guide
- Drawing the graph for the equation of a circle Study Guide
- Key features of a cubic graph Study Guide
- Key features of a quadratic graph Study Guide
- Key features of an exponential graph Study Guide
- Problem solving with non-linear graphs Study Guide
Browse all guides in the Year 10 Maths guide library.