A videoke machine can be rented for ₱1000 for three days, but for thefourth day onwards and additional cost of ₱400 per day is added. Representthe cost of renting a videoke machine as a piecewise function.
y = 1000 for x <= 3
y = 1000 + 400x for x > 3
II. A videoke machine can be rented for P 1000 for 3 days, but the fourth day onwards, an additional cost of P 400 a day is a added. Represent the cost of renting a videoke machine as a piecewise function of the number of days it is rented. *
Math
Renting a videoke machine can be represented as a piecewise function:
Let's call the number of days rented as x.
For the first 3 days, the cost is ₱1000, so we have:
Cost(x) = ₱1000, for 1 ≤ x ≤ 3
For the fourth day onwards, an additional cost of ₱400 per day is added, so we have:
Cost(x) = ₱1000 + ₱400(x - 3), for x > 3
Therefore, the cost of renting a videoke machine as a piecewise function is:
Cost(x) = ₱1000, for 1 ≤ x ≤ 3
Cost(x) = ₱1000 + ₱400(x - 3), for x > 3
Remember, renting a videoke machine may help improve your singing skills, but it won't improve your comedic timing!
To represent the cost of renting a videoke machine as a piecewise function, we need to define different expressions for different ranges of days.
Let's break it down into two cases:
Case 1: Renting for three days
In this case, the cost is a flat rate of ₱1000 for three days. So, the function for this case is:
Cost = ₱1000
Case 2: Renting for four days and more
Once the rental exceeds three days, the cost of renting is ₱400 per additional day. So, for each additional day after the third day, the cost increases by ₱400. The function for this case is:
Cost = ₱1000 + ₱400 * (number of additional days)
Let's combine the two cases to form the piecewise function:
Cost of Renting a Videoke Machine (C) =
- ₱1000, if number of days <= 3
- ₱1000 + ₱400 * (number of days - 3), if number of days >= 4
In the piecewise function, the first line represents Case 1, where the cost is ₱1000 for three days. The second line represents Case 2, where the cost increases by ₱400 for each additional day after the third day.