In this context, we can interpret the variables and terms as they relate to the man's journey:
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Domain (0 ≤ x ≤ 4.16): The domain represents the range of time (or perhaps a measure of distance) over which the man's journey takes place. In this case, 'x' could represent time in seconds or any other unit of measure related to the duration of his run. The limits indicate that the journey occurs from the start (x = 0) until the man completes his trip (x = 4.16).
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Range (2 ≤ y ≤ 14): The range describes the heights above the ground that the man reaches during his run. It starts at a height of 2 meters (the height at which he begins) and goes up to a maximum height of 14 meters (the top of the hill). This means that at some point during his run, he ascends to this peak height before descending back.
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Interval of Increase (0 ≤ x ≤ 2): This interval indicates the period during which the man is ascending, running up the hill. In this scenario, for values of 'x' from 0 to 2, the height (y) is increasing from 2 meters to the maximum height of 14 meters. It suggests that during this time, he is actively climbing.
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Interval of Decrease (2 ≤ x ≤ 4.16): Following his ascent, this interval represents the period in which the man is descending, coming back down to the ground. For values of 'x' from 2 to 4.16, the man's height (y) decreases from 14 meters back down to 0 meters. At the end of this interval, he has returned to the ground level (y = 0 meters), completing his journey.
In summary, the story describes a man's journey starting at 2 meters above ground, increasing to a peak of 14 meters while he runs uphill, and then returning back down to ground level, with the specified intervals delineating the periods of ascent and descent.