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There are infinitely many types of functions.
For example:
Discrete function,
Continuous functions,
Differentiable functions,
Monotonic functions,
Odd functions,
Even functions,
Invertible functions.
Another way of classifying them gives:
Logarithmic functions,
Inverse functions,
Algebraic functions,
Trigonometric functions,
Exponential functions,
Hyperbolic functions.
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