1. The problem is to analyze the cubic function $f(x)$ based on the given graph description. 2. The graph shows a cubic-like curve with a local maximum near $x = -1.5$ at about $y = 3$ and a local minimum near $x = 1.5$ at about $y = -3$. 3. The curve crosses the $x$-axis near $x \approx -2$, $x = 0$, and $x \approx 2.5$. 4. To understand the behavior, recall that a cubic function generally has the form $$f(x) = ax^3 + bx^2 + cx + d$$ and can have up to two turning points (local max and min). 5. The local maximum and minimum correspond to points where the derivative $f'(x) = 3ax^2 + 2bx + c$ equals zero. 6. The zeros of the function are the $x$-intercepts where $f(x) = 0$. 7. From the graph, the function increases to a local max near $(-1.5, 3)$, decreases to a local min near $(1.5, -3)$, and then increases again. 8. This behavior is typical of a cubic with positive leading coefficient $a > 0$. 9. The approximate roots are $x \approx -2$, $0$, and $2.5$. 10. This analysis helps understand the shape and key points of the cubic function based on the graph. Final answer: The cubic function $f(x)$ has local max near $(-1.5, 3)$, local min near $(1.5, -3)$, and roots near $-2$, $0$, and $2.5$.