Here are functions representing each situation: 1. M(x) = {10x if x < 50 450 + 8(x - 50) if x ≥ 50} 2. C(x) = {150x if x ≤ 15 140x if x > 15} 3. V(x) = (20-2x)(8-2x)x 4. R(d) = {50 + 10(d - 300) if d > 300 50 if d ≤ 300} 5. F(h) = {100 + 20(h - 3) if h ≤ 10 500 if h > 10}

3. A relation is any set of ordered pairs where
the set of all first coordinates is called the
domain of the relation and the set of all
second coordinates is called the range of the
relation. Aside from ordered pairs, a relation
may be represented in four other ways: (1)
table, (2) mapping diagram, (3) graph, and (4)
rule.

4. A function is a special type of relation. It
is a relation in which every element in the
domain is mapped to exactly one element
in the range. Furthermore, a set of ordered
pairs is a function if no two ordered pairs
have equal abscissas.

5. Using functional notation, we can write
f(x) = y, read as “f of x is equal to y.” In
particular, if (1, 2) is an ordered pair
associated with the function f, then we say
that f (2) = 1.

6. Example 1. Determine whether the
following relations are functions or not
given the set of ordered pairs
A. {(0, 3), (1, 4), (2, 5), (3, 6), (4, 7)}
B. {(1, 2), (2, 3), (2, 0), (3, 5)}

7. Example 2. Tell whether or not each table of
values represents a function.

8. Example 3: Consider the mapping diagram below,
which one describes a function?

9. Example 4. Determine whether each graph
represents a function.

10. Example 5: Which of the following equations
describe a function?
a. x2 + y = 8 b. x2 + y2 = 9

11. Functions as representations of real-life situations.
Functions can often be used to model real 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
Since each meal costs P40, then the cost
is C(x) = 40x.

12. Example 2: State a function P that will describe
the total distance of a student when he runs 5
km per day at the end of 5 days.
Answer:
Since each day makes him 5 km, then the distance
function is 𝑃(𝑥)=5𝑥.

13. Example 3: In a certain city, the Philippine Statistics Office has
recorded a total population of 680, 000 in the year 2018. The
population increases at the rate of 0.25% annually. Determine
an equation that represents the population with respect to the
number of years after 2018. Suppose the rate of increase is
constant.
The equation will be of the form, 𝑃=𝑎(1+𝑟) 𝑛 such that a is the initial
population, r is the rate of increase and n is the time in years and p is
the population. Hence, the we have the function 𝑃=680,000(1.0025)𝑛
.

14. A piecewise function is a function that contains
at least two equations “pieces” each of which
depends on the value of the independent
variable or the domain.

15. Example 4: Driving lessons require a rental car fee of P
500. 00 for the first 8 km. and for every kilometer added
charges an additional fee of P 50.00. Express a piecewise
function for the problem.

16. Example 5: An online seller charges a certain amount for
the shipping fee of purchased products/items. For orders 10
or fewer items, she charges P20.00 each, P15.00 per item for
orders of 20 or fewer but more than 10 items, and P10.00
per item for orders of more than 20 items. Write a function
representing the cost 𝑓 for the number of 𝑥 items/products.

17. A. identify the following whether function or
not
1. (-3, -6), (1, 0), (3, 6), (6, 12)
2. (2, 5), (2, 7), (2, 9), (2,1)
3.

18. 4.
5.
6.

19. B. Represent the following into function
1.A person is earning P600 per day to do a certain
job. Express the total salary S as a function of the
number n of days that the person works.
f(S) = 600x

20. A jeepney ride costs P8.00 for the first 4 kilometers,
and each additional integer kilometer adds P1.50 to
the fare. Use a piecewise function to represent the
jeepney fare in terms of the distance (d) in
kilometers
F(d) ={
8.00
8 +1.5(d)
If 0 < d ≤ 4
If d > 4

21. Application of Functions
Monthly Salary: When you receive your monthly salary what you are been paid
is a function of the hourly pay rate and the number of you worked for that
month.
Income Tax: When calculating your income tax you will observe that you made
use of a mathematical function why your salary serve as your input and your tax
result is the output. You will observe that the higher your income the higher your
income tax.
Compound interest: when interest calculated on an investment the compound
interest is a function of initial investment, interest rate, and time or interval of the
investment.
Supply and demand: when trying to forecast the price of product and service
daily we mad use of functions. The price of the product or services acts as the
input why the demand serves as the output of the function. As price goes up,
demand goes down and vice versa.

22. LET’S GENERALIZED!
What is function?
How do we represent functions in real life
situations?

23. Directions: Give a function that represents each situation. [2 points
each]
1.Mang Ambo, a mango farmer, sells ripe mangoes either per piece
or bulk. He sells mangoes at P10.00 each for orders less than 50
pieces and P450.00 for a bulk of 50 pieces and P8.00 for each
excess mango after that. Write the required piecewise function.
2.A certain Liquor is sold for P150.00 each. With an increasing
public demand, a vendor decides to sell it for P140.00 each if
someone buys more than 15 bottles. Express the cost with respect
to the number of bottled liquors sold.

24. 3. A rectangular box is to be made from a piece of
cardboard 20 cm long and 8 cm wide by cutting out
identical squares with side x from the four corners and
turning up the sides. Define a function representing the
volume of the box.
4. A horseback riding charges P50.00 for the first 300
meters and additional P10.00 for a ride greater than
300 meters. Express the function describing the
amount of horseback riding.

25. 5. Rental car charges P100.00 for the first three hours
and an excess of P20.00 for each hour (or a fraction
of it) after that. If you rent a car for more than ten
hours, a fee of P500.00 shall be charged. Represent
the rental car fee in piecewise function.