Non-linear graphs

 Any relationship containing powers of \(y\) or \(x\), or an operator other than an addition or multiplication of a constant, will not be a straight line. These are non-linear graphs.


Key Concepts

 Parabola

The \(x\) term is squared.

  Inverse proportion

The axes act as asymptotes, which means the graph does not cross them:

\(y = {1 \over x}\)

  Sinousoidal graphs

Periodic functions in which a pattern repeats over time (\(\sin x\) or \(\cos x\)).

Essentials

 Exponential

The rate of change is proportional to the current value (more of this in Capacitors and Nuclear Decay).

HINT: Do not use the term 'exponential' to describe any increasing gradient - it is only true in special cases.

Exponential decay graphs can be distinguished from inversely proportional graphs as they have a finite value at time zero, meaning that they cross the vertical axis. In equal times, the quantity falls by an equal ratio.

  Logarithmic

The inverse of an exponential relationship.

Test Yourself

Use quizzes to practise application of theory.


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