The graph you uploaded appears to be that of a polynomial function, likely of degree 4 because it has three turning points. Based on the shape and orientation of the graph, we can infer that it is a quartic function (degree 4 polynomial) that opens downward.

Key observations from the graph:

1. The graph crosses the x-axis at approximately $x = -7$, $x = -1$, and $x = 4$.
2. There are turning points at around $x = -5$, $x = 2$, and $x = 7$.
3. The graph seems to have a general negative leading coefficient since the end behavior shows the function goes to $-\infty$ as $x$ approaches both $+\infty$ and $-\infty$.

General form of the function:

Given these characteristics, we can model the function as a factored polynomial: $f(x) = a(x + 7)(x + 1)(x - 4)(x - c)$ where $c$ would be the fourth root, and $a$ is a leading coefficient to adjust for the vertical stretch.

Since the graph has a turning point near $x = 2$, we might estimate that the factor related to $c$ is near this point. Also, the negative leading coefficient $a$ suggests that the function opens downward, so we need to adjust this accordingly.

If we assume the factor $x - c$ affects the shape but keep the general form, the function becomes: $f(x) = -k(x + 7)(x + 1)(x - 4)^2$ where $k$ is a constant.

This is a general form for the function that could fit the graph's behavior. However, the exact form would require further refinement based on precise turning points.

Would you like more details on how to refine the equation or have any further questions? Here are some related topics you might be interested in:

1. How can we determine the exact turning points of the graph?
2. How does the leading coefficient influence the graph of a polynomial?
3. What is the significance of repeated roots in a polynomial?
4. How do you factor and expand polynomials from their roots?
5. How can we approximate the function from graph behavior using software?

Tip: The degree of a polynomial directly correlates to its number of turning points (at most $n - 1$ turning points for degree $n$).