Based on the given graph and the equation provided, we previously determined that the roots of $f(x) = x^2 - 9$ are $x = -3$ and $x = 3$.

We also identified that the graph of $y = g(x)$ intersects the x-axis at the same points, $x = -3$ and $x = 3$, which means these are the common roots between $f(x)$ and $g(x)$.

Given the multiple-choice answers: A. $f$ e $g$ têm as mesmas raízes. B. $f$ e $g$ têm uma raiz em comum, mas cada uma delas tem outra raiz não compartilhada. C. $f$ e $g$ não têm raízes em comum.

The correct answer is: A. $f$ e $g$ têm as mesmas raízes.

Would you like any further details or have any questions?

Here are 5 questions you might want to ask:

1. How can we find the intersection points of two different functions analytically?
2. Can you explain the graphical representation of roots for quadratic functions?
3. What methods can be used to solve quadratic equations?
4. How can we determine the vertex of a quadratic function?
5. What are the key features of a parabola and how are they useful in solving equations?

Tip: When working with quadratic functions, always check both roots by substituting back into the original equation to ensure they satisfy it.