Question

In this section we discussed examples of ordinary, everyday functions: population is a function of time, postage cost is a function of package weight, water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.

Short answer

Example 1- A vehicle moves at a speed of \(60\;{\rm{mi/h}}\) for 2 hours. The distance covered by the vehicle is the function of time t. If \(d\left( t \right)\) is the distance function, then value of t represents its domain.

The domain of the function \(d\left( t \right)\) is \(0 \le t \le 2\).

The range of the function is \(0 \le d\left( t \right) \le 120\).

Example 2- In a school there are N students in the annual function after midnight.

The domain of the function is \(0 \le t \le 24\).

The range of the function is \(0 \le N \le k\).

Example 3- The wage of a person is $8 per hour. And in a week, the maximum working hours are 30 hours.

Wage P is a function of the number of hours. The domain of the function is \(\left( {0,30} \right)\) and the range of the function is \(\left\{ {0,\,2.00,\,4.00,......,238.00,\,240.00} \right\}\).

Step-by-step solution

Write the first example

A vehicle moves at a speed of \(60\;{\rm{mi/h}}\) for 2 hours. The distance covered by the vehicle is the function of time t. If \(d\left( t \right)\) is the distance function, then value of t represents its domain.

So, domain of the function \(d\left( t \right)\) is \(0 \le t \le 2\).

And the range of the function is \(0 \le d\left( t \right) \le 120\).

The following figure represents the graph of the function.

Write the second example

In a school, there are N students in the annual function after midnight.

So, the domain of the function is \(0 \le t \le 24\).

Let k (an integer) represent the maximum number of students in the school. So, the range of function is \(0 \le N \le k\).

The following figure represents the graph of the function.

Write the third example

The wage of a person is $8 per hour, and in a week, the maximum working hours are 30 hours.

Wage P is a function of the number of hours. The domain of the function is \(0 \le t \le 30\) and the range of the function is \(\left\{ {0,\,2.00,\,4.00,......,238.00,\,240.00} \right\}\).

The following figure represents the graph of the function.