Rational Points on Graph of Exponential Function

Theorem
Consider the graph of the exponential function in the real Cartesian plane $\R^2$:
 * $f := \left\{ {\left({x, y}\right) \in \R^2: y = e^x}\right\}$

The only rational point of $f$ is $\left({0, 1}\right)$.

Proof
From Exponential of Rational Number is Irrational, $r \in \Q_{\ne 0} \implies e^r \in \R - \Q$.

Thus, apart from the point $\left({0, 1}\right)$, when $x$ is rational, $e^x$ is not.

Hence the result.