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The problem asks to determine which statement about the function \( y = f(x) \) is correct based on the given sign chart (bảng biến thiên). Let's break it down:

### Sign chart interpretation:
- The \( x \)-values are split into three intervals: \( (-\infty, -1) \), \( (-1, 1) \), and \( (1, +\infty) \).
- The chart shows the behavior of \( y' \) (the derivative of \( f(x) \)) in these intervals:
  - For \( x \in (-\infty, -1) \), \( y' > 0 \) (the function is **increasing**).
  - For \( x \in (-1, 1) \), \( y' < 0 \) (the function is **decreasing**).
  - For \( x \in (1, +\infty) \), \( y' > 0 \) (the function is **increasing** again).
- The function has critical points at \( x = -1 \) and \( x = 1 \), where it changes from increasing to decreasing and vice versa.

Now, let's analyze the options:

**A. Hàm số nghịch biến trên khoảng \( (1, +\infty) \).**
- This states that the function is decreasing on \( (1, +\infty) \).
- From the chart, we can see that the derivative is positive on \( (1, +\infty) \), so the function is increasing here, not decreasing. Therefore, **A is incorrect**.

**B. Hàm số đồng biến trên khoảng \( (-\infty, -2) \).**
- This states that the function is increasing on \( (-\infty, -2) \).
- The chart shows the function is increasing on the interval \( (-\infty, -1) \), but it doesn't mention specifically \( (-\infty, -2) \). However, we can assume that within \( (-\infty, -1) \), the function is increasing. Therefore, **B is correct** for this range.

**C. Hàm số nghịch biến trên khoảng \( (-\infty, 1) \).**
- This states that the function is decreasing on \( (-\infty, 1) \).
- The chart shows that the function is increasing for \( (-\infty, -1) \), but decreasing on \( (-1, 1) \), so this statement is only partially true. Therefore, **C is incorrect**.

**D. Hàm số đồng biến trên khoảng \( (-1, +\infty) \).**
- This states that the function is increasing on \( (-1, +\infty) \).
- From the chart, the function is decreasing on \( (-1, 1) \) and increasing on \( (1, +\infty) \), so this statement is only partially correct. Therefore, **D is incorrect**.

### Conclusion:
The correct answer is **B**.

Do you need more details, or do you have any questions? 

Here are some related questions:
1. How can we determine the behavior of a function from its derivative?
2. What is the importance of critical points in understanding a function's behavior?
3. How do the signs of the first derivative relate to the increasing or decreasing nature of a function?
4. What does the second derivative tell us about the concavity of a function?
5. Can you explain how local maxima and minima are found using the first derivative test?

**Tip:** When analyzing a function's behavior, the sign of its derivative tells you whether the function is increasing (positive derivative) or decreasing (negative derivative).

Cho hàm số y = f(x) có bảng biến thiên như sau: Mệnh đề nào sau đây đúng?

Learn how to determine the increasing and decreasing intervals of a function using its derivative. This problem uses the first derivative test to analyze the behavior of the function y = f(x) based on a sign chart. Suitable for students in Grades 10-12.

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