To determine the smallest value of $x$ for which $f(x) = g(x)$, let's analyze the intersection points of the two graphs provided in the image.

1. Identify the Intersections: The problem requires finding the x-coordinate of the first intersection between the curves $f(x)$ (parabola) and $g(x)$ (line). By examining the graph, we can see the intersection points.

2. Read the Graph: Looking closely, the smallest x-coordinate at which $f(x)$ and $g(x)$ intersect appears to be around $x = -3$.

Therefore, the smallest value of $x$ for which $f(x) = g(x)$ is: $x = -3$

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. What are the coordinates of all intersection points between $f(x)$ and $g(x)$?
2. How can we algebraically solve for the intersections if the equations of $f(x)$ and $g(x)$ are known?
3. What is the significance of the intersection points in a real-world context?
4. How would the graph change if we shifted $f(x)$ up by 2 units?
5. What is the slope of $g(x)$, and how does it affect the intersection points?

Tip: When analyzing graphs, always check the axes and scale carefully to accurately read values.