Final answer:
The function representing the height of a ball that has been dropped from a rooftop as a function of time is the one that cannot be classified as increasing, since its trajectory is governed by gravity causing it to fall.
Step-by-step explanation:
The function that cannot be classified as increasing is the 'height of a ball that has been dropped from a rooftop as a function of time'. When a ball is dropped, gravity accelerates it towards the earth, meaning the function representing its height over time is decreasing. In contrast, a person's weight on a diet consisting primarily of fast food is likely to increase, a skydiver's altitude decreases then stabilizes once the parachute opens, and the air pressure in a balloon decreases as air leaks out.
In relation to the provided information, ' moving an object to a greater height without acceleration' and 'carrying an object without acceleration at the same height' both imply a constant or increasing height function, which would classify these as non-decreasing, but not necessarily strictly increasing.
Using the concept of air density and altitude, we understand that as altitude increases, air density, and consequently air pressure decreases, an inverse relationship that is a hallmark of a decreasing function, as illustrated in the example of the air density decreasing with the increase in altitude of a climbing mountain.