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For what value of x is ​g(x)equalsnegative 2​?

To determine the value of \( x \) for which \( g(x) = -2 \), we need to find the point on the graph where the function \( g(x) \) intersects the line \( y = -2 \).

Upon analyzing the graph, we observe the following:

- The function \( g(x) \) intersects the line \( y = -2 \) at the point where the x-coordinate is \(-2\).

Therefore, the value of \( x \) for which \( g(x) = -2 \) is \(\boxed{-2}\).

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. What is the slope of the line segment from \( x = -6 \) to \( x = -2 \)?
2. What is the slope of the line segment from \( x = -2 \) to \( x = 3 \)?
3. What are the coordinates of the point where \( g(x) \) intersects the y-axis?
4. What is the value of \( g(x) \) when \( x = 3 \)?
5. For what values of \( x \) is \( g(x) = 0 \)?
6. What is the domain of the function \( g(x) \)?
7. What is the range of the function \( g(x) \)?
8. What are the x-intercepts and y-intercepts of the function \( g(x) \)?

**Tip:** When analyzing piecewise linear functions on a graph, pay attention to the points where the slope changes and note these critical points for a complete understanding of the function's behavior.

Learn how to find the value of x where g(x) equals negative 2 (g(x) = -2) with a detailed explanation. This problem involves graphing functions and finding intersections with lines. Suitable for high school students studying algebra and functions.

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