Looking at the graph, it appears that the polynomial function intersects the x-axis at three points: $x = -2$, $x = 0$, and $x = 2$. This suggests that the function has roots at these points.

The least-degree polynomial that fits this graph would have factors corresponding to these roots. The general form of the polynomial can be written as:

$f(x) = a(x + 2)(x)(x - 2)$

Where $a$ is a constant that affects the vertical stretch or compression of the graph.

To determine the value of $a$, we can observe the graph’s behavior as it tends to infinity. Since the graph rises on the right and falls on the left, the degree of the polynomial must be odd (which it is). Looking at the general shape, it appears that $a = 1$, so the polynomial is:

$f(x) = (x + 2)(x)(x - 2)$

This is a cubic polynomial of the least degree that corresponds to the graph.

Would you like more details on how to analyze graphs like this? Here are some follow-up questions to explore:

1. How can we determine the behavior of the function at infinity by looking at the graph?
2. How do we identify the degree of a polynomial from its graph?
3. What is the significance of the turning points of a polynomial function?
4. How do we find the value of $a$ from the graph?
5. What is the role of multiplicities in determining the shape of the graph?

Tip: Always check the number of turning points and the general direction of the graph to help determine the degree of the polynomial!