volume_mute
Formal Definition of the Graph of a Function
publish date: 2026/05/23 18:30:37.197160 UTC
volume_mute
If \(f: A \to B\) is a function, its graph is defined as:
Correct Answer
\(\{(a, f(a)) \mid a \in A\}\)
Explanation
The graph of \(f\) is the set \(\{{(a, f(a)) \mid a \in A\}}\) — all ordered pairs where the first coordinate is a domain element and the second is its image. This is a subset of \(A \times B\). When \(A, B \subseteq \mathbb{R}\), these pairs become points in the Cartesian plane, which may form isolated points or a continuous curve depending on the domain.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012