The graph of the function $y = x^3$ represents a cubic curve that intersects the origin and exhibits a characteristic S-shape.

To elaborate, the graph of $y = x^3$ is classified as a cubic function, which is a specific type of polynomial graph. This function is distinguished by its unique S-shape, indicating the presence of a point of inflection at the origin, specifically at the coordinates $(0, 0)$. At this point of inflection, the graph undergoes a change in curvature. For positive values of $x$ (i.e., $x > 0$), the graph ascends steeply towards the right, while for negative values of $x$ (i.e., $x < 0$), it descends sharply towards the left.

As $x$ increases, the corresponding value of $y$ rises rapidly, and conversely, as $x$ decreases, $y$ falls dramatically. This behavior implies that as one moves away from the origin in either direction along the x-axis, the absolute values of $y$ become increasingly large or increasingly small. Moreover, the graph is symmetric with respect to the origin; this means that if it were to be rotated 180 degrees around the origin, it would appear unchanged.

Unlike quadratic functions, which exhibit parabolic shapes and possess maximum or minimum points, the cubic function $y = x^3$ has no such extrema. Its graph is a smooth, continuous curve that extends infinitely in both the positive and negative directions along the x and y axes. Understanding the shape and properties of this graph is essential for visualizing the behavior of cubic functions and distinguishing them from other polynomial functions.