Question

Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that W = 35T + 700 gives W as a function of I during the next 80 minutes.

Answer 1

The domain of a function refers to the set of all the input values of a function and the range is the possible output given by the function.

In other words, domain refers to all values of the independent variable that will yield a defined output and the range refers to the defined output values of the dependent variable.

From the question, W is the total amount of water in the pond and this value is dependent on the total number of minutes that water has been added (T). Therefore, the total number of minutes the water has been added is the domain and the amount of water in the pond is the range.

The function is given to be:

`W=35T+700`

T is given to be the time up to 80 minutes. Since we cannot have any time less than 0 minutes, the domain will be:

`0\leq T\leq80`

The lower boundary for the range will be:

`\begin{gathered} W=35(0)+700 \\ W=700 \end{gathered}`

The upper boundary will be:

`\begin{gathered} W=35(80)+700 \\ W=3500 \end{gathered}`

The range will be:

`700\leq W\leq3500`