Functions are elements of your input vectors. The number of functions is equal to the number of nodes in the input network layer.
If you used a neural network to classify people as men or women, things like height, weight, hair length, etc. would be such functions. Each of them would have an initial value in meters, kilograms, etc. and then will be normalized and centered at zero (inside the function) before being presented to the system.
So this guy:
height: 1,5 m
weight: 70 kg
hair length: 0.1 m
Initially, the vector [1.5, 70, 0.1] will be presented, and then after the preliminary processing (there should be other elements in the data set ...) with something like [-0.2, 0.4, .05]
The image features of the letter can be as simple as the grayscale values in pixels. Other functions can be generated by processing images and extracting parameters from power spectra or finding edges, etc. To learn more about this, find information about image processing and feature extraction.
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