Answer :
To determine over which intervals the function \( f(x) \) is less than zero (\( f(x) < 0 \)), we need to carefully examine the given choices and compare them with the provided information that \( f(x) < 0 \) over the interval \((-∞, -3)\).
We are asked to find another interval from the given options where \( f(x) < 0 \) holds true. The given options are:
1. \((-2.4, -1.1)\)
2. \((-3, -1.1)\)
3. \((-1.1, 2)\)
4. \((-1.1, 0.9)\)
Since \( f(x) \) is less than zero (\( f(x) < 0 \)) in the interval \((-∞, -3)\), we are looking for a range that we can logically infer to follow after the interval \((-∞, -3)\).
Upon examining the intervals:
1. \((-2.4, -1.1)\):
- This interval ranges from \(-2.4\) to \(-1.1\), which falls to the right of \(-3\).
- It is possible for \( f(x) \) to be negative in this interval depending on the behavior of the function after \(-3\).
2. \((-3, -1.1)\):
- This interval starts exactly at \(-3\) and goes to \(-1.1\).
- If \( f(x) \) is negative immediately before \(-3\) over the interval \((-∞, -3)\) and continues to the right, then it is reasonable to infer that \( f(x) \) could also be negative in this interval.
3. \((-1.1, 2)\):
- This interval spans from \(-1.1\) to \(2\), moving into positive territory.
- This wider range seems less likely to denote areas where \( f(x) < 0 \) unless we had more specific details indicating this.
4. \((-1.1, 0.9)\):
- This interval starts at \(-1.1\) and ends at \(0.9\).
- Similar to the third option, but a bit smaller in range.
- The specifics of when \( f(x) \) changes sign would influence this, but less likely given available information.
Based on these considerations, the most logical and supported interval where \( f(x) < 0 \) holds, in addition to \((-∞, -3)\), is:
[tex]\[ \boxed{(-3, -1.1)} \][/tex]
We are asked to find another interval from the given options where \( f(x) < 0 \) holds true. The given options are:
1. \((-2.4, -1.1)\)
2. \((-3, -1.1)\)
3. \((-1.1, 2)\)
4. \((-1.1, 0.9)\)
Since \( f(x) \) is less than zero (\( f(x) < 0 \)) in the interval \((-∞, -3)\), we are looking for a range that we can logically infer to follow after the interval \((-∞, -3)\).
Upon examining the intervals:
1. \((-2.4, -1.1)\):
- This interval ranges from \(-2.4\) to \(-1.1\), which falls to the right of \(-3\).
- It is possible for \( f(x) \) to be negative in this interval depending on the behavior of the function after \(-3\).
2. \((-3, -1.1)\):
- This interval starts exactly at \(-3\) and goes to \(-1.1\).
- If \( f(x) \) is negative immediately before \(-3\) over the interval \((-∞, -3)\) and continues to the right, then it is reasonable to infer that \( f(x) \) could also be negative in this interval.
3. \((-1.1, 2)\):
- This interval spans from \(-1.1\) to \(2\), moving into positive territory.
- This wider range seems less likely to denote areas where \( f(x) < 0 \) unless we had more specific details indicating this.
4. \((-1.1, 0.9)\):
- This interval starts at \(-1.1\) and ends at \(0.9\).
- Similar to the third option, but a bit smaller in range.
- The specifics of when \( f(x) \) changes sign would influence this, but less likely given available information.
Based on these considerations, the most logical and supported interval where \( f(x) < 0 \) holds, in addition to \((-∞, -3)\), is:
[tex]\[ \boxed{(-3, -1.1)} \][/tex]
