# Functions as Representations of Real-Life Situations

```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 &lt; 𝒙 ≤ 𝟑
𝒊𝒇 𝒙 &gt; 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