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1. Lesson 1 : Relation and Function
Set of ordered pairs (x,y)
Set of ordered pairs (x,y)
Every “x” must be loyal/unique

2. Lesson 1 : Relation and Function
Daniel
Enrique
Gerald
Kathryn
Liza
Julia
Kim
x y
EXAMPLE #1
Daniel
Enrique
Gerald
Kathryn
Liza
Julia
Kim
x y
EXAMPLE #2
Every “x” must be loyal/unique

3. Lesson 1 : Representation of Function
1. Through Set of ordered pairs (x,y)
Examples:
1. {(1,2),(3,4),(5,6),(7,8)}
2. {(2,2),(4,4),(6,6),(8,8)}
3. {(4,3),(5,4),(4,5),(5,6)}
F
F
NF

4. Lesson 1 : Representation of Function
1. Through Mapping Diagram (x,y)
Example #1:
Function
1
3
5
7
2
4
6
8
X (Domain) Y (Range)

5. Lesson 1 : Representation of Function
1. Through Mapping Diagram (x,y)
Example #2:
Function
2
4
6
8
2
4
6
8
X (Domain) Y (Range)

6. Lesson 1 : Representation of Function
1. Through Mapping Diagram (x,y)
Example #3:
Not Function
4
5
3
4
5
6
X (Domain) Y (Range)

7. Lesson 1 : Representation of Function
1. Through Graphing
Example #1:
y
1. {(1,2),(3,4),(5,6),(7,8)}
x
1 2 3 4 7
5 6 8
1
2
3
4
5
6
7
8

8. Lesson 1 : Representation of Function
1. Through Graphing using vertical line test
Example #1:
Function

9. Lesson 1 : Representation of Function
1. Through Graphing using vertical line test
Example #2:
Not
Function

10. Act. 1 : Determine if the following is a function or not
1. {(3,4),(8,8),(12,13),(16,17)}
2. {(3,4),(7,4),(13,13),(16,16)}
3. 3
5
7
9
3
5
7
4.
5.

11. Lesson 2: Set Builder Notation
N- Natural numbers
I – Integers
Q – Rational numbers
R – Real numbers
1, 2,3,4, …, +∞
- ∞ ,…,-4,-3,-2,-1,0,1, 2,3,4, …, +∞
- ∞ ,…,-4,-3,-2,
−1
2
,-1,0,
1
2
,1, 2,3,4, …, +∞
- ∞ ,…,-4,-3,-2,
−1
2
,-1,0,
1
2
,1, 2,3,4, …, +∞
𝛱 𝑎𝑛𝑑 √

12. 𝑥 𝑥 𝜖ℝ} 𝑆𝑒𝑡 𝑜𝑓 𝑎𝑙𝑙 𝑥 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑥 𝑖𝑠 𝑎𝑛
𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
{}
𝜖
ℝ
𝑆𝑒𝑡
𝑆𝑢𝑐ℎ 𝑡ℎ𝑎𝑡
𝑒𝑙𝑒𝑚𝑒𝑛𝑡
𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

13. 𝐿𝑖𝑛𝑒𝑎𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛
𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛
𝑆𝑞𝑢𝑎𝑟𝑒 𝑟𝑜𝑜𝑡 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛
y= 2x + 4
y =𝑥2 − 2𝑥 + 1
𝑦 = 𝑥
𝑅𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛 y =
2𝑥
𝑥2

14. Identify the domain for each
relation using set builder notation
1.y= 3x - 2
2.Y=3𝑥2
− 4𝑥
3. 𝑦 = 𝑥 + 1
4. y =
2
𝑥−1
𝑥 𝑥𝜖𝑅}
𝑥 𝑥𝜖𝑅}
𝑥 𝑥𝜖𝑅, 𝑥 ≥ −1}
𝑥 𝑥𝜖𝑅, 𝑥/1}

15. Identify the domain for each relation
using set builder notation
1.y =
2
2𝑥+4
2.Y=𝑥2
− 𝑥
3. 𝑦 = 2𝑥
4. y =
3
2𝑥
𝑥 𝑥𝜖𝑅, 𝑥/−2}
𝑥 𝑥𝜖𝑅}
𝑥 𝑥𝜖𝑅, 𝑥 ≥ 0}
𝑥 𝑥𝜖𝑅, 𝑥/0}

16. Activity 2: Identify the domain for each
relation using set builder notation
1.y =
1
𝑥2−1
2.y = 6𝑥 − 2
3. 𝑦 = 𝑥 + 1
4. y =
1
2𝑥−7

17. Activity 2: Identify the domain for each
relation using set builder notation
1.y =
1
𝑥2−1
2.y = 6𝑥 − 2
3. 𝑦 = 𝑥 + 1
4. y =
1
2𝑥−7
𝑥 𝑥𝜖𝑅, 𝑥/ −1, +1}
𝑥 𝑥𝜖𝑅}
𝑥 𝑥𝜖𝑅, 𝑥/3.5}
𝑥 𝑥𝜖𝑅, 𝑥 ≥
1
3
}

18. Evaluating Function
Replacing the variable in the function or
“Pulihan si X ug value”
Example:
f(x)= 3x where x=2
f(x)= 3(2)
f(x)= 6

19. Evaluating Function
Example: Evaluate the following function at x = -2
1. f(x) = 11x-2
3. h(x) = 𝑥 + 3
2. g(x) = 𝑥2
− 6𝑥 + 9

20. Evaluating Function
Example: Evaluate the following function at x= x-1
1. f(x) = -4x +1
2. g(x) = 2𝑥2
− 2x

21. Evaluating Function
Example: Given f(x)= 𝒙𝟐
+ 𝟒𝒙 + 𝟒 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓:
1. f(3)
2. f(-2)
3. f(0)

22. 1. f(x)= −𝟑𝒙 + 𝟒
Activity 3: Evaluate the following function at x= -3
2. f(x)= −𝟐𝒙
3. f(x)= 𝒙𝟐
− 𝟐𝒙
Given that f(x)= 𝒙𝟐
+ 𝟑𝒙 − 𝟒, 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓:
4. f(-2) =
5. f(-1) =

23. A computer shop charges P20.00 per hours for the first two hours and
an additional P10.00 per hour for each succeeding hour.
Find how much you would pay if you used one of their computers for:
1.) 40 minutes

24. A computer shop charges P20.00 per hours for the first two hours and
an additional P10.00 per hour for each succeeding hour.
Find how much you would pay if you used one of their computers for:
1.) 3 hrs

25. A computer shop charges P20.00 per hours for the first two hours and
an additional P10.00 per hour for each succeeding hour.
Find how much you would pay if you used one of their computers for:
1.) 150 minutes

26. Lesson 4: Operations on Functions
Let f and g be functions
f − 𝑔 𝑥 = 𝑓 𝑥 − 𝑔(𝑥)
f + 𝑔 𝑥 = 𝑓 𝑥 + 𝑔(𝑥)
f • 𝑔 𝑥 = 𝑓 𝑥 • 𝑔(𝑥)
𝑓
g
𝑥 =
𝑓 𝑥
g 𝑥

27. Use the following functions below
for example 1
𝑓 𝑥 = 𝑥 − 3
p 𝑥 = 2𝑥 + 7
v 𝑥 = 𝑥2
+ 4𝑥 − 5
g 𝑥 = 𝑥2
− 1
ℎ 𝑥 =
𝑥 + 7
2 − 𝑥
Example 1: Determine the value
of the following functions
a.) 𝑣 + 𝑔 𝑥
b.) 𝑓 • 𝑝 𝑥
c.) 𝑓 + 𝑔 𝑥
d.) 𝑝 − 𝑓 𝑥
e.)
𝑣
g
𝑥

28. Activity 4: Determine the value of the following functions
given that 𝑓 𝑥 = 3𝑥 − 6 and g 𝑥 = 𝑥 − 2
1.) f + 𝑔 𝑥
2.) f − 𝑔 𝑥
3.) f • 𝑔 𝑥
4.)
𝑓
g
𝑥

29. Lesson 5: Composite Functions
The composite function denoted by
f ∘ 𝑔 𝑥 = 𝑓 𝑔(𝑥)