To determine the approximate value of $x$ when $g(x) = 2$ using the graph, we need to find the points on the graph where the $y$-coordinate (which represents $g(x)$) is equal to 2.

1. Locate $g(x) = 2$ on the graph: This corresponds to a horizontal line at $y = 2$.

2. Identify the intersection points: Find the $x$-coordinates where the graph of $g(x)$ intersects this horizontal line.

Looking at the graph:

• The graph intersects the line $g(x) = 2$ at approximately $x = -6$ and $x = 5$.

These are the approximate $x$ values where $g(x) = 2$.

Answers:

• $x \approx -6$
• $x \approx 5$

These correspond to the given choices in the multiple-choice answers.

Would you like more details or have any questions?

Here are five related questions to expand on this topic:

1. What is the significance of finding the roots of the function in a real-world scenario?
2. How can you estimate other function values using a graph?
3. How does the slope of the graph at different points affect the values of $g(x)$?
4. How do transformations (like shifting or stretching) affect the graph of $g(x)$?
5. How would you solve for $x$ if the equation was given algebraically rather than graphically?

Tip: When interpreting a graph, always pay close attention to where the function crosses key values (like $y = 0$ for roots or any other given $y$ value). This helps in approximating solutions quickly.