Answer:
1. "As x decreases without bound, f(x) increases without bound."
This statement implies that as the value of x becomes increasingly negative (approaching negative infinity), the function f(x) grows larger and larger without any upper limit. In other words, as x approaches negative infinity, f(x) diverges towards positive infinity.
2. "As x increases without bound, f(x) approaches the line y = -4."
This statement suggests that as x becomes increasingly positive (approaching positive infinity), the function f(x) approaches the horizontal line y = -4. This means that for very large positive values of x, f(x) gets arbitrarily close to -4 but never actually reaches it.
3. "As x decreases without bound, f(x) approaches zero."
According to this statement, as x becomes increasingly negative (approaching negative infinity), the function f(x) tends towards zero. In other words, for very large negative values of x, f(x) gets arbitrarily close to zero but never actually reaches it.
4. "As x decreases without bound, f(x) approaches the line y = 4."
This statement states that as x becomes increasingly negative (approaching negative infinity), the function f(x) approaches the horizontal line y = 4. This means that for very large negative values of x, f(x) gets arbitrarily close to 4 but never actually reaches it.
Based on these statements, we can conclude that only statements 1 and 3 are true:
- As x decreases without bound, f(x) increases without bound.
- As x decreases without bound, f(x) approaches zero.
Statements 2 and 4 are contradictory because they suggest different limiting behaviors for f(x) as x approaches negative infinity. Therefore, we cannot consider both of them to be true simultaneously.
In summary, as x decreases without bound, f(x) increases without bound and approaches zero. The statements about f(x) approaching the lines y = -4 and y = 4 are not consistent with each other.
Explanation: