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Year 10 - Maths

Key features of an exponential graph

Non-linear graphs

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 an exponential graph.

Key Notes

  • A exponential graph has a distinct shape.
  • An exponential graph has one asymptote.
  • The laws of indices explain where this asymptote is.

Vocabulary To Learn

  • Exponential: The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.
  • Asymptote: An asymptote is a line that a curve approaches but never touches.

Common Mistakes To Avoid

  • $$y=b^x$$ will reach zero; the curve will touch the $$x$$ axis eventually.

3 Quick Questions (With Answers)

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

A exponential graph has a distinct shape. An exponential graph has one asymptote.

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

The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: $$y=b^x$$ will reach zero; the curve will touch the $$x$$ axis eventually. Correction: Get pupils to input large absolute $$x$$ values to appreciate that no matter how small the $$y$$ value it is still a fraction greater than zero.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.