How to denote the graph of a function $f$ over an interval $[a;b]$?

Question

Is there a conventional notation to write it? I am thinking in writing it as $f_{[a;b]}$.

Answer 1

For $f : A \to B$: $$ G_f = \{ (x, f(x)) \in A \times B \mid x \in A \} $$ I am not sure if there is a different notation for some interval $A = [a, b]$.

Answer 2

The explicit construction of a function $f:A \rightarrow B$ is a functional relation from $A$ to $B$. So $f \subset A \times B$. A pair $(a,b) \in f$ defines the notation $f(a)=b$.

If by graph of $f$ you mean the set of all points $(x,f(x))$ in the "plane", then the graph is precisely $f$.

If you need to restrict the domain of the function, then your $f_{[a;b]}$ notation does the job, although it may not be conventional.