Question

The functions in Example 6 and Exercises 52 and 53(a) are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life.

Short answer

The win of a candidate as a function of votes and the opening of a grocery store according to time are real-life examples of the step function.

Step-by-step solution

First real-life example of the step function

The step functions are the function in which the independent variable varies with steps and gives different values of the dependent variable for different steps.

The win of a candidate in the election as a function of the number of votes is a real-life example of a step function because the candidate requires the number of votes greater than or equal to the minimum number of necessary votes for winning.

Suppose a candidate contests an election. If a candidate gets more than or equal to the p number of votes then he is declared winning otherwise he losses the electron. The function for the win of the candidate is given below:

\(f\left( x \right) = \left\{ \begin{aligned}{l}W,x \ge p\\L,x < p\end{aligned} \right.\)

Here, W and P denote the win and loss respectively of the election for the candidate.

Second real-life example of the step function

The grocery stores in the markets open and close according to the timing of the market so the function for closing and opening of store as a function of time is also an example of the step function.

Suppose a grocery store opens at 9:00 AM and closes at 6:00 PM. It can be shown by the following equation.

\(f\left( t \right) = \left\{ \begin{aligned}{l}O,\,\,\,9\;{\rm{AM}} \le t \le 6\;{\rm{PM}}\\C,\,\,\,t < 9\;{\rm{AM}}\;or\;t > 6\;{\rm{PM}}\end{aligned} \right.\)

Here, O and C represent the opening or closing of the grocery store.