To solve this problem, we firstly need to find out how many minutes will it take to completely drain the tub.
We have a tub that has initially 15 gallons of water in it, and the draining rate is 0.5 gallons per minute. This means that each minute, half a gallon of water is exiting the tub.
To find out the time it will take to empty the tub, we just need to divide the initial amount of water by the draining rate. Let’s calculate: 15 gallons divided by 0.5 gallons per minute equals 30 minutes. So, after 30 minutes, the tub will be empty.
Now let's determine the range of the function. The range of a function is the possible output or y-values that we can get for the function.
In this case, our function g(x)=15 - 0.5x represents the amount of water in the tub at any given time x, with x being the number of minutes passed.
As time passes, the amount of the water in the tub is decreasing from the initial 15 gallons. After 0 minutes, we have 15 gallons, and after 30 minutes, we have 0 gallons of water left, the tub is empty. So, the possible values for g(x) or the amount of gallons of water in the tub range from 0 to 15.
To conclude, the time it takes to completely drain the tub is 30 minutes, and the range of the function for this situation is from 0 to 15.