To find the interval where $f(x) \geq g(x)$, let's analyze the graph and focus on the intersection and behavior of the two functions.

1. Intersection point: The graphs of $f(x)$ (green) and $g(x)$ (blue) intersect at approximately $(x = 1, y = 2)$. This is the point where $f(x) = g(x)$.

2. Behavior of the functions:

   • To the left of the intersection point (for $x < 1$): The green line (representing $f(x)$) is above the blue line (representing $g(x)$). Hence, $f(x) > g(x)$.
   • To the right of the intersection point (for $x > 1$): The green line is below the blue line, meaning $f(x) < g(x)$.

Thus, the interval where $f(x) \geq g(x)$ occurs when $x \leq 1$, including the point where they intersect.

Final Answer:

The solution is $(-\infty, 1]$.

Would you like more details on how to interpret the graph or solve this?

Here are five questions to expand this concept:

1. How do you find the intersection points of two linear equations algebraically?
2. How can you determine the slopes of linear functions from a graph?
3. What does it mean when one function is above another on a graph?
4. How do you express inequalities in interval notation?
5. What role does the intersection point play in solving inequalities involving two functions?

Tip: When working with graphs of functions, always focus on key points like intersections and the behavior of the functions on either side of these points.