1. Let's start by understanding what asymptotic notations are: they are mathematical notations used to describe the behavior of functions as the input grows large, commonly used in computer science to analyze algorithm efficiency. 2. The most common asymptotic notations are Big O ($O$), Omega ($\Omega$), and Theta ($\Theta$), which respectively describe upper bound, lower bound, and tight bound growth rates. 3. To graph these notations, consider a function $f(n)$ representing the algorithm's running time and another function $g(n)$ as a comparison for growth rate. 4. For Big O notation $f(n) = O(g(n))$, this means there exist constants $c > 0$ and $n_0$ such that for all $n \ge n_0$, $f(n) \le c \cdot g(n)$. Graphically, $f(n)$ will lie on or below some scaled version of $g(n)$ beyond $n_0$. 5. Similarly, for Big Omega notation $f(n) = \Omega(g(n))$, $f(n)$ is on or above some scaled version of $g(n)$ beyond $n_0$. 6. For Big Theta notation $f(n) = \Theta(g(n))$, $f(n)$ is bounded both above and below by constant multiples of $g(n)$ after $n_0$, so the graphs of $f(n)$ and $g(n)$ grow at the same rate asymptotically. 7. To graph asymptotic notation precisely, plot $f(n)$ and $c \cdot g(n)$ for some constants $c$ and visually verify that $f(n)$ stays within the defined bounds beyond $n_0$. 8. No direct formula to plot one symbol exists but plotting $f(n)$ versus $g(n)$ with appropriate scaling and domain demonstrates asymptotic relationships. The key idea is comparing growth trends on a graph, focusing on large $n$.