The document defines functions and relations, explains how to use the vertical line test to identify functions, and discusses representing real-life situations using functions, including piecewise functions. It provides examples of determining the domain and range of various relations and identifying graphs that represent functions. Finally, it gives an example of defining a piecewise function to model a tricycle fare based on distance and poses a word problem to write a piecewise function for weekly pay based on hours worked with overtime pay.

2. SPECIFIC
OBJECTIVES
Define function and relations.
Explain on how to use the vertical line
test.
Representing real-life situations using
functions, including piecewise functions.

3. ACTIVITY 1:

4. It is the set of first coordinates.
RANGE DOMAIN ABSCISSA
It is the set of second coordinates.
RANGE DOMAIN ABSCISSA

5. Find the domain and range of the
given ordered pairs.
{(1,-1), (2,-3), (0,5), (-1,3), (4,-5), (-1,5), (4,-4)}

9. 10
20
30
40
50
15
25
35
45
55
INPUT OUTPUT
FUNCTION

10. 2
4
3
20
30
40
INPUT OUTPUT
NOT A
FUNCTION

11. A
B
C
D
X
Y
Z
INPUT OUTPUT
FUNCTION

12. A graph represents a function if and only if
each vertical line intersects the graph at most
once.

13. y = 2x + 1
y = x^2 – 2x + 2
x^2 + y – 4 = 0
x^2 + y^2 = 1 y =
𝟐𝒙+𝟏
𝒙 −𝟏
y = 𝒙 + 𝟏

14. 1. { (-7,4), (8, 3), (-7,7), (20, 8), (5,9),
(1,3) }
2. { (10,9), (3, 6), (2,-2), (-2, 5) }
3. { (a,b), (c,d). (c,e), (f,g), (x,y)
4. { (6,-9), (-6,9), (10, 12), (11,11) }

17. 9. y + x^2 = 6
10. y^2 + x^2 = 9

18. PIECEWISE FUNCTION

23. A tricycle ride cost 15 pesos for the first 1
kilometer, and each additional 1 kilometer adds 1
peso to the fare. Use a piecewise function to
represent the tricycle fare in terms of the
distance d in kilometers.
Solution: The input value is distance and
the output is the cost of the tricycle fare. If
F(d) represents the fare as a function of
distance, the function can be represented
as follows.

24. Group activity: Solve me!
Problem:
You have a summer job that pays time and a half for
overtime. That is, if you work more than 40 hours per week,
your hourly wage for extra hours is 1.5 times your normal
hourly wage of 50 pesos.
1. Write a piecewise function that gives your weekly pay P in
terms of the number of hours h you work.
2. How much will you get paid if you work 50 hours?