Let's analyze the relationship between the graphs of $f(x)$ and $g(x)$ using the provided information.

1. Graph transformation: Looking at the two graphs, it seems that $g(x)$ is a reflection of $f(x)$ over the y-axis. This reflection is a horizontal flip. The main indicator is that the overall shape of $g(x)$ is similar to $f(x)$, but it has been mirrored over the y-axis.

2. Points comparison: The graphs indicate that:

   • $f(x)$ ends at $(4, 6)$, while $g(x)$ ends at $(2, 6)$. This suggests a horizontal compression. Specifically, the x-coordinates have been scaled by a factor, possibly indicating a horizontal transformation.

3. Reflection and scaling: Since we notice that the x-values are halved when going from $f(x)$ to $g(x)$, the x-coordinates have likely been multiplied by $\frac{1}{2}$.

4. Effect on points: We should also check specific values. For instance, if $f(-2)$ corresponds to some value, we can see if $g(-1)$ shares the same value, which would confirm the horizontal compression.

Thus, based on the given graphs:

• The graph of $g(x)$ is a horizontal reflection of the graph of $f(x)$.
• The x-values have been halved.
• This is the result of a horizontal compression by a factor of 2.

Would you like more detailed steps on how these transformations are applied to functions?

Here are five related questions you might find useful:

1. How can we mathematically express the horizontal reflection and compression in a transformation equation?
2. What other types of transformations (e.g., vertical shifts) might apply to similar problems?
3. If $f(x)$ is shifted vertically, how would $g(x)$ be affected by that?
4. How would the derivative of $f(x)$ change under a horizontal compression?
5. Can we generalize this transformation for all types of functions, or is it specific to the given case?

Tip: When identifying transformations between two graphs, always compare key points (like intercepts and endpoints) to understand scaling or reflections.