Final answer:
The union of three intervals is represented by combining all the numbers that belong to any of the three given intervals: (-42, -16] ⋃ (3, 24) ⋃ [44, 75).
Step-by-step explanation
To find the union of the three given intervals, we need to identify the combined set of values that are covered by any of the intervals. The union includes all values that are in at least one of the intervals.
The union of three intervals is represented by combining all the numbers that belong to any of the three given intervals. In this case, the union of the intervals (-42,-16], (3,24), and [44,75) would include all numbers that are either greater than -42 and less than or equal to -16, or greater than 3 and less than 24, or greater than or equal to 44 and less than 75.The union involves all values that appear in any of these intervals
So, the union of the three intervals would be (-42, -16] ⋃ (3, 24) ⋃ [44, 75).