Equation field guide
Functions: inputs become outputs
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Rule, input, output
In y = f(x), x is an input and y is the output the function produces for that input. f names the rule or model; it is not a number multiplied by x.
If the function has several inputs, f(x, t) is determined by the pair x and t. The article may call them features, coordinates, parameters, or conditions.
Parameters
A subscript or parameter such as fθ(x) identifies which member of a family of functions is used. In machine learning, θ often names learned parameters, but the article must establish whether that convention applies.
Changing an input and changing the function’s parameters are different operations. One evaluates the same rule at a different point; the other changes the rule itself.
Domain and range
The domain is the set of allowed inputs; the range is the set of outputs actually obtained. A formula may be valid only for part of the possible inputs.
When reading a source, check what the input represents and whether the output is a measured quantity, a prediction, a score, or a probability.