The task involves analyzing the graph of two functions $y = f(x)$ (black curve) and $y = g(x)$ (blue curve) and determining the number of roots of the equation $f(x) = g(x)$. This means finding the number of intersection points between the two curves.

From the graph:

1. There is 1 intersection to the left of the y-axis.
2. There are 3 intersections to the right of the y-axis.

Thus, the total number of roots is:

$1 + 3 = 4$

The answer is: 4.

Let me know if you want further details or have more questions! Here are five related questions to deepen your understanding:

1. How can we algebraically solve $f(x) = g(x)$ if the equations of the curves are known?
2. What is the significance of the intersection points in real-world applications?
3. How do we determine the behavior of functions graphically (e.g., asymptotes, maxima, minima)?
4. How can symmetry help reduce the effort in analyzing such graphs?
5. How would this process differ if $f(x)$ or $g(x)$ were piecewise-defined functions?

Tip: Always verify intersection points both graphically and algebraically if possible for accuracy.