Consider a function which has both variables and parameters, such as
$$
y(x) = 3x^2 + ax + b,
$$
where $a$ and $b$ are the paramters (constants) for any one realisation, but $x$ is a variable. What is the correct notation to use to indicate the function with $a$, for example, taking a certain value?
Should it be something like the "evaluated at" symbol, like this:
$$
y(x)\rvert_{a=2} = 3x^2+2x+b
$$
or would it be written as an argument like this:
$$
y(x,a=2) = 3x^2+2x+b.
$$
Or is there another accepted way that I am not aware of?
Thank you.
Best Answer
If you plan on specifying the parameter $a$, it might be best to choose beforehand a notation that reflects that intention. For example, either of the notational choices $y(x,a)=3x^2+ax+b$ or $y_a(x)=3x^2+ax+b$ makes it easy to show what you want to show. (And similar notational choices can be used for $b$, with or without $a$.)