Answer:
The domain of a function represents the set of all possible input values for the function. In this case, the function w(x) = -30x + 210 represents the amount of water in the tank as a function of time.
To determine the domain of the function, we need to consider what values x can take on. Since x represents the number of hours, it cannot be negative, as we cannot have a negative amount of time. Therefore, the minimum value for x is 0.
Additionally, we need to consider the maximum value for x. The tank initially contains 210 gallons of water, and water is being drained at a rate of 30 gallons per hour. So the maximum number of hours we can have is the time it takes to drain all the water in the tank. We can find this time by setting w(x) = 0 and solving for x:
-30x + 210 = 0
-30x = -210
x = -210/-30
x = 7
Therefore, the maximum value for x is 7.
Explanation:
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