To determine which function is negative for the interval \([-1, 1]\), we need to evaluate where each function falls below the x-axis (where \(y < 0\)) within that interval.
From the descriptions provided:
1. **First Function:**
- Minimum value at (\(-1, -2\))
- Crosses x-axis at (\(-2.5, 0\)) and (0.5, 0)
- Crosses y-axis at (0, \(-1\))
For this function, since it crosses the x-axis at \(0.5\) and has a minimum point of \((-1, -2)\), it is negative from \(-2.5\) to \(0.5\). Therefore, it is negative in the interval \([-1, 0.5]\), which overlaps with \([-1, 1]\).
2. **Second Function:**
- Minimum value at \((0, -2)\)
- Crosses x-axis at \((-1.5, 0\)) and (1.5, 0)
For this function, it is negative between \((-1.5, 0)\) and (1.5, 0). Therefore, it is negative in the complete interval \([-1, 1]\).
3. **Third Function:**
- Maximum value at \((0, 2)\)
- Minimum value at \((1.5, -2.75)\)
- Crosses x-axis at \((-0.6, 0)\) and (0.6, 0)
For this function, it is negative between \((-0.6, 0)\) and (0.6, 0). Therefore, it is negative only in the interval \([-0.6, 0.6]\), which is within \([-1, 1]\).
4. **Fourth Function:**
- Maximum value at \((-1.25, 4)\)
- Minimum value at \((1.5, -3.5)\)
- Crosses x-axis at \((-1.75, 0\)), (0.75, 0), and (1.75, 0)
For this function, it is negative between \(0.75\) and \((next positive crossing point 1.75)\). Therefore, it is negative from \(0.75\) onwards within \([1.75\]). This does not make it negative at all within \([-1, 1]\).
**Result:**
The functions which are negative for at least part of the interval \([-1, 1]\) are:
- The First Function
- The Second Function
- The Third Function
Which function is negative for the interval [–1, 1]?
On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2.5, 0) and (0.5, 0), and the y-axis at (0, negative 1).
On a coordinate plane, a curved line with a minimum value of (0, negative 2), crosses the x-axis at (negative 1.5, 0) and (1.5, 0).
On a coordinate plane, a curved line with a maximum value of (0, 2) and a minimum value of (1.5, negative 2.75), crosses the x-axis at (negative 0.6, 0) and (0.6, 0).
On a coordinate plane, a curved line with a maximum value of (negative 1.25, 4) and a minimum value of (1.5, negative 3.5), crosses the x-axis at (negative 1.75, 0), (0.75, 0), and (1.75, 0), and crosses the y-axis at (0, 2).
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