How the graph of function is parameterized curve in the plane?

Question

Consider general function $f:A\rightarrow\mathbb{R}^{n}$. Show that the graph of f in the plane is exactly the parameterized curve $F(t)=(t,f(t))$

Answer 1

If $f$ is discontinuous, it is difficult to say about the curve. For example, the graph of a discontinuous additive function $a:\mathbb{R}\to\mathbb{R}$ is dense on the whole plane. What kind of a curve is the graph of such a function?

Nevertheless we always have

$$ \text{Graph}(f)=\bigl\{\bigl(t,f(t)\bigr)\colon t\in A\bigr\}. $$