Range

The range of a function is the set of all output values produced by the inputs in its domain.

Imagine an empty water tank that fills at a constant rate of 20 liters per minute until it reaches its maximum capacity of 1,000 liters.

We can model the volume of water in the tank with the function W of t equals 20 times t. Here, t is the time in minutes, and W of t is the volume of water in liters.

Since the tank starts empty and fills at 20 liters per minute, it reaches 1,000 liters after 50 minutes. So, for this model, the domain is all values of t from 0 to 50.

As time increases from 0 to 50 minutes, the volume of water increases continuously from 0 to 1,000 liters. So, the range is all values of W of t from 0 to 1,000 liters, including both endpoints.

We restrict this model to the first 50 minutes because, beyond that point, the formula predicts a volume greater than the tank's capacity. The tank's capacity limits the domain, and the function's outputs over that domain form the range.