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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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