Question

A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L=3D+300 gives L as a function of D. The crew can work for at most 70 days.Identify the correct description of the values in both the domain and the range of the function. Then, for each, choose the most appropriate set of valuesProvided picture for the choices

Answer 1

Step 1

The domain of a function refers to all the values that go into a function. The domain of a function is the set of inputs accepted by the function. The output values are called the range.

Step 2

From the domain in this question, the number of days the crew has worked will determine the length of the road in miles. The domain is the independent quantity in a function. The number of days the crew has worked is independent of the length of the road. It does not depend on it.

Hence, the answer is;

`\begin{gathered} Domain-Number\text{ of days the crew has worked} \\ Range-Length\text{ of the road\lparen in miles\rparen} \end{gathered}`

Step 3

Choose the most appropriate set of values. The crew can work for at most 70 days. Therefore;

`The\text{ domain will be all real numbers from 0 to 70}`
`\begin{gathered} The\text{ range will be;} \\ L=3D+300 \\ L=3(70)\text{ + 300=210+300=510\lparen Maximum range value\rparen} \\ L=3(0)+300=300\text{ \lparen minimum range value\rparen} \end{gathered}`

The range will be;

`The\text{ set of real all numbers from 300 to 510}`