How to represent the costing of renting the karaoke machine using piecewise funtion?

Question

During holidays karaoke machine is very in demand because Filipinos loves to sing. Jocelyn’s karaoke machine can be rented 2, 000 pesos for the first three days and additional 550 pesos for the succeeding days.

Answer 1

A piecewise function is a function that is defined by different formulas over different parts of its domain. To represent the cost of renting a karaoke machine using a piecewise function, you can define a function that has different formulas for different ranges of time.

For example, suppose the karaoke machine costs $50 per day to rent, and you want to represent this cost using a piecewise function. You can define the function as follows:

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In this example, the function f represents the cost of renting the karaoke machine for a certain number of days t. The function has a different formula for each range of t, depending on how many days the machine is rented.

You can continue this pattern for as many days as you want, defining a new formula for each additional day. For example, if the cost is $50 per day and you want to represent the cost of renting the machine for up to 7 days, you can define the function as follows:

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This function represents the cost of renting the karaoke machine for any number of days up to 7 days.