Question

Determine both domain and range

The set of ordered pairs (t, m) where m is
the remaining mass of a 500-gram sample
of a radioactive substance that has been
decaying for t hours.

Answer 1

The domain is t ≥ 0 and the range is 0 ≤ m ≤ 500.

Step-by-step explanation:

The given set of ordered pairs (t, m) represents the remaining mass of a radioactive substance that has been decaying for t hours. The domain of this set is the range of values that t can take, which can be any non-negative real number since time cannot be negative. So, the domain is t ≥ 0.

The range of this set is the range of values that m can take, which represents the remaining mass. Since the substance is decaying, the remaining mass cannot exceed the initial mass or be negative. Thus, the range is 0 ≤ m ≤ 500.

Answer 2

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis