Final answer:
The correct representation in interval notation for the union of the intervals (-8, 3) U (-9, -4) is (-9, 3), which is option b.
Correct option is B
Step-by-step explanation:
The question asks to represent the union of two intervals, (-8, 3) and (-9, -4), in interval notation. The interval (-8, 3) includes all numbers between -8 and 3 but does not include -8 and 3 themselves, whereas (-9, -4) includes numbers between -9 and -4, not including -9 and -4 either. When we union these two intervals, we need to look at the numbers that are covered by either of the intervals. Here, the intervals partially overlap. The interval (-9, -4) covers a part of the interval (-8, -4), so when combined, the lowest number we have is -9 and the highest is 3.
Therefore, the interval notation for the union of these two intervals is (-9, 3). This corresponds to option b. So, the correct representation in interval notation for the union of intervals (-8, 3) U (-9, -4) is (-9, 3).