\begin{tabular}{l} Given that the polynomial $$ f(x) $$ has degree 7 , which of the following most accurately describes the number of turning points \ of $$ f(x) $$ ? \ Select the correct answer below: \ The graph of $$ f(x) $$ has at least 8 turning points. \ The graph of $$ f(x) $$ has at most 7 turning points. \ The graph of $$ f(x) $$ has at least 7 turning points. \ The graph of $$ f(x) $$ has at least 6 turning points. \ The graph of $$ f(x) $$ has at most 8 turning points. \ The graph of $$ f(x) $$ has at most 6 turning points. \ \hline\end{tabular}

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To determine the number of turning points of a polynomial function $$ f(x) $$ of degree 7, we can use the following rule:

- A polynomial of degree $$ n $$ can have at most $$ n - 1 $$ turning points.

Given that the degree of the polynomial $$ f(x) $$ is 7, we can calculate the maximum number of turning points:

$$
\text{Maximum turning points} = 7 - 1 = 6
$$

This means that the graph of $$ f(x) $$ can have at most 6 turning points.

Now, let's analyze the options provided:

1. The graph of $$ f(x) $$ has at least 8 turning points. (Incorrect)
2. The graph of $$ f(x) $$ has at most 7 turning points. (Incorrect, since it can have at most 6)
3. The graph of $$ f(x) $$ has at least 7 turning points. (Incorrect)
4. The graph of $$ f(x) $$ has at least 6 turning points. (Incorrect, it can have fewer)
5. The graph of $$ f(x) $$ has at most 8 turning points. (Correct, but not the most accurate)
6. The graph of $$ f(x) $$ has at most 6 turning points. (Correct and most accurate)

Thus, the most accurate description of the number of turning points of $$ f(x) $$ is:

**The graph of $$ f(x) $$ has at most 6 turning points.**
The graph of $$ f(x) $$ has at most 6 turning points.

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