To determine the intervals where \( f(x) < 0 \), we analyze the x-intercepts where the function crosses the x-axis, as well as the given minimum and maximum values.
The x-intercepts are at:
- \( x = -3 \)
- \( x = -1.1 \)
- \( x = 0.9 \)
This means that \( f(x) \) changes from negative to positive at these points. Specifically:
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From \( -\infty \) to \( -3 \): Since the function must be negative in this range (as it hasn't crossed the x-axis yet).
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Between the x-intercepts:
- From \( -3 \) to \( -1.1 \) is negative.
- From \( -1.1 \) to \( 0.9 \) the function is positive (as it crosses the x-axis from below).
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From \( 0.9 \) to \( +\infty \): After crossing at \( 0.9 \), the function remains positive.
The function crosses the y-axis at \( (0, -3) \), meaning it is negative at \( x = 0 \), confirming that it is below the x-axis between \( -3 \) and \( -1.1 \).
Conclusion:
Thus, \( f(x) < 0 \) over the following intervals:
- \( (-\infty, -3) \)
- \( (-3, -1.1) \)
So the complete statement is: \( f(x) < 0 \) over the intervals \( (-\infty, -3) \) and \( (-3, -1.1) \).
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