The document discusses functions and piecewise functions. It defines a function as relating an input to an output and gives examples of functions in real life. Piecewise functions are functions defined by different expressions in different parts of the domain. The document contains examples of determining if a relation is a function based on sets of ordered pairs and graphs. It also discusses representing real world situations using functions and piecewise functions.

1. Ms. Pauline Misty M. Panganiban
General Mathematics

2. What we are about to learn…
a. Define functions, and piece-wise functions
b. Determine whether a relation is a function
or not;
c. Represent real-life situations using
functions, including piece-wise functions.

3. What will happen to the following if I’m
going to put this into this machine
(factory)?
1.Fish
2.Beef
What about if the machine will produce it
product using f(x) = x + 3
1.4
2.5
3.-2

5. Functions
 Functions relate an input to an
output
Functions in real life:
Output: Score in the test
Input: No. of hours studied

6. Functions
Functions in real life:
 Give another real-life situations
involving functions

7. Functions
Illustration of Functions:
b. mapping or arrow diagram
a. set of ordered pair
c. graphing

8. Functions
a. set of ordered pair
1. {(3,2), (4,0), (5,1), (2,3)} Function
2. {(1,2), (0,3), (1,6), (5,4)}
3. {(3,4), (3,0), (3,1), (3,3)}
4. {(4,2), (3,2), (6,2), (5,2)}
Not Function
Not Function
Function

9. Functions
a. set of ordered pair ( x, y )
x - First element Domain
y - Second Element Range
Independent variable
Dependent variable

10. Functions
b. diagram
3
4
5
Function
One-to-One
Relation
a
b
c
2
3
6
9
4
3
2
3
6
2
3
6
2
3
Function Not Function Not Function
Many-to-One
Relation
One-to-Many
Relation
Not all elements
are represented

11. Functions
c. graphing

12. Functions
c. graphing

13. Determine if the following sets of ordered pairs, table of
values, and equations represent a function.
1.{(-4,2), (0,9), (-4,-8), (4,5), (-1, 10), (11, 15)}
2.{(math, science), (math, English), (math, economics),
(math, history)}
3.f(x) = x2
4.f(x) = /2x + 9/

14. Piece-wise Functions
 Functions in pieces

15. Piece-wise Functions

16. Piece-wise Functions

17. Piece-wise Functions

18. Write a piece-wise function from the given problem.
A Doctor's fee is based on the length of time.
• Up to 6 minutes costs Php 300
• Over 6 to 15 minutes costs Php 500
• Over 15 minutes costs Php 500 plus Php 100 per minute
above 15 minutes

19. A. Determine if the following sets of ordered pairs, table of values,
and equations represents a function.
1.{(5,9), (0,-3), (3,1), (11,-7)}
2.{(apple, banana), (apple, guyabano), (apple, guava), (apple,
pineapple)}
3.f(x) = x4
4.x = y2
5. X 2 6 2 8
f(x) 4 8 9 10

20. B. Problem solving using piecewise function
A merchant sells rice at Php 45.00 a kilo. If however, a buyer
buys more than 150 kilos of rice, the merchant gives a 10%
discount.
1. If x represents the number of kilos of rice purchased,
express the amount to be paid by f(x).
2. How much should be paid for 100 kilos of rice?
3. How much should be paid for 200 kilos of rice?

21. A Function f is a correspondence between two sets, the
domain and the range, such that for each value in the
domain, there corresponds exactly one value in the
range.
A Piece-wise function is a function which consists of
two or more functions in a specified domain.

22. Types of Functions
1.Polynomial function
2.Constant function
3.Linear function
4.Quadratic function
5.Cubic function

23. Determine if the following sets of ordered
pairs, table of values, and equations represent
a function.
1. {(-4,2), (0,9), (-4,-8), (4,5), (-1, 10), (11, 15)}
2.{(math, science), (math, English), (math,
economics), (math, history)}
3.f(x) = x2
4.f(x) = /2x + 9/

24. Functions
Answer Me:
Is this relation a function?
1. {(1,3),(2,3),(3,3)}
2. {(2,3),(2,3),(4,3)}
3. {(-3,3),(-2,3),(-
5,3)}
4. {(1,4),(2,4),(3,4)}
Yes
No
Yes
Yes

25. Functions
Answer Me:
Is this relation a function?
Yes
No

26. Functions
Answer Me:
Is this graph a function?
Yes
No

27. Functions
Answer Me:
Is this graph a function?

28. Functions
Answer Me:
Find the value:
1. f(x) = 3x2 - 4x + 9
x = 0, x = -2
2. h(x) = 4x3 - 6x - 12
3. g(x) = 5x + 4
4. f(x) = x2 + 5x
f(0) = 9 f(-2) = 29
h(0) = -12
f(0) = 0
g(0) = 4
h(-2) = 32
g(-2) = -6
f(-2) = -6

29. Activity:
• Function: (Oh
Yes!)
• Not Function: (Oh
No!)
1. {(-2,3),(2,3),(-3,3)}
2. {(3,3),(2,2),(4,4)}
3. {(1,8),(1,5),(1,3)}
4. {(7,3),(8,3),(5,3)}
Oh Yes!
Oh Yes!
Oh No!
Oh Yes!

30. Activity:
• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!
Oh Yes!
Oh No!

31. Activity:
• Function: (Oh Yes!) • Not Function: (Oh
No!)
Oh Yes! Oh No! Oh Yes!
Oh No!

32. Activity:
• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!
Oh Yes!
Oh No!

33. Functions
Assessment:
A. Which of the following are functions
1. {(4,3),(-4,3),(3,3)}
2. {(2,5),(4,4),(2,3)}
Function
Not Function
Not Function
Function
3. 4
.