1. **Problem Statement:** We are given a polynomial function $f(x)$ graphed with specific characteristics and asked to identify which statement is NOT true about $f(x)$. 2. **Given Statements:** - The range of $f(x)$ is $(-\infty, \infty)$. - $(x + 6)$ is a factor of $f(x)$. - $x = 3$ is a triple root of the function. - As $x \to +\infty$, $f(x) \to -\infty$. 3. **Analyzing the Graph:** - The graph crosses the x-axis near $-6$, so $(x + 6)$ is likely a factor. - The graph crosses the x-axis near $1$ and $6$, and has a local maximum between $3$ and $4$. - The graph starts high at $x = -7$ and ends low at $x = 7$, indicating the leading term has negative leading coefficient and odd degree. 4. **Check the range:** - The graph goes from about $50$ down to about $-60$, and since it is a polynomial of odd degree, it extends to $\pm \infty$ in $y$ as $x \to \pm \infty$. - So the range is indeed $(-\infty, \infty)$. 5. **Check $(x + 6)$ factor:** - Since the graph crosses the x-axis near $-6$, $(x + 6)$ is a factor. 6. **Check if $x=3$ is a triple root:** - The graph does not cross or touch the x-axis at $x=3$; it has a local maximum between $3$ and $4$ but does not cross the axis there. - Therefore, $x=3$ is NOT a root, let alone a triple root. 7. **Check end behavior:** - As $x \to +\infty$, $f(x) \to -\infty$ matches the graph going down on the right. **Conclusion:** The statement "$x=3$ is a triple root of the function" is NOT a characteristic of $f(x)$. **Final answer:** $x=3$ is NOT a triple root of $f(x)$.