Functions as Representations
of Real-Life Situations.
Franklin E. Benitez
Functions can often be used to model
real-life situations. Identifying an
appropriate functional model will lead to
a better understanding of various
phenomena.
Example 1. Give a function 𝑪 that can
represent the cost of buying 𝒙 meals if one
meal costs P40.00.
Solution: Since each meal costs P40.00,
then the cost function is
𝑪(𝒙) = 𝟒𝟎𝒙.
Example 2. A videoke machine can be rented for
P1000 for three days, but for the fourth day
onwards, an additional cost of P400 per day is
added. Represent the cost of renting a videoke
machine as a piecewise function of the number of
days it is rented.
𝒇 𝒙 =
𝟏𝟎𝟎𝟎,
𝟏𝟎𝟎𝟎 + 𝟒𝟎𝟎(𝒙 − 𝟑),
𝒊𝒇 𝟎 < 𝒙 ≤ 𝟑
𝒊𝒇 𝒙 > 𝟑
Seatwork
1. A user is charged P300 monthly for a particular mobile plan,
which includes 100 free text messages. Messages in excess of
100 are charged P1 each. Represent the amount a consumer
pays each month as a function of the number of messages m sent
in a month.
2. A jeepney ride costs P8.00 for the first 4 kilometers, and each
additional integer kilometer adds P1.5 to the fare. Use a
piecewise function to represent the jeepney fare in terms of the
distance (d) in kilometers.
ASSIGNMENT:
The cost of hiring a catering service to serve
food for a party is P150 per head for 20
persons or less, P130 per head for 21 to 50
persons, and P110 per head for 51 to
100persons. For 100 or more persons, the
cost is at P100 per head. Represent the total
cost as a piecewise function of the number of
attendees of the party.