To determine which statement is true about the function \( f(x) \), specific information about the function such as its equation, graph, or key points where it changes sign is required. Without this information, it's not possible to definitively verify the statements provided.
Let's analyze the statements logically based on general comprehension:
1. **f(x) < 0 over the intervals (–infinity, –2.7) and (0.8, infinity).**
- This statement suggests \( f(x) \) is negative for very large negative values of \( x \) until \( x = -2.7 \) and after \( x = 0.8 \) to very large positive values of \( x \).
2. **f(x) < 0 over the intervals (–infinity, –2.7) and (–1, 0.8).**
- This statement suggests \( f(x) \) is negative for very large negative values of \( x \) until \( x = -2.7 \) and also between \(-1\) and \(0.8\).
3. **f(x) > 0 over the intervals (–infinity, –2.7) and (–1, 0.8).**
- This statement suggests \( f(x) \) is positive for very large negative values of \( x \) until \( x = -2.7 \) and also between \(-1\) and \(0.8\).
4. **f(x) > 0 over the intervals (–infinity, –1) and (0.8, infinity).**
- This statement suggests \( f(x) \) is positive for very large negative values of \( x \) until \( x = -1 \) and after \( x = 0.8 \) to very large positive values of \( x \).
Without the specific behavior of \( f(x) \), a general guessing cannot ascertain which statement is true. If we infer hypothetical intervals based on implied logic, we notice:
- If \( f(x) < 0 \) for certain intervals, \( f(x) \) must cross the x-axis (i.e., pass through zero) to change sign.
- It is not typical for a function to change from negative to positive then back to negative without additional critical points in between unless specified as such (not shown here).
To make an informed guess typically:
- Functions often have zero crossings at critical points or roots.
- Assuming standard polynomial behavior, trying to align with known roots or values is key.
Thus, as purely speculative without full function details provided, the most likely true statement for common scenarios, assuming subtle basic polynomial properties and intervals, could be:
**f(x) < 0 over the intervals (–infinity, –2.7) and (–1, 0.8).**
Purely speculative based on typical behavior of simple polynomial functions. Accurate analysis requires the complete function definition or graph depiction.
Which statement is true about the given function?
f(x) < 0 over the intervals (–infinity, –2.7) and (0.8, infinity).
f(x) < 0 over the intervals (–infinity, –2.7) and
(–1, 0.8).
f(x) > 0 over the intervals (–infinity, –2.7) and
(–1, 0.8).
f(x) > 0 over the intervals (–infinity, –1) and
(0.8, infinity).
1 answer
1 answer