2. RELATION
i. TWO SETS ARE INVOLVED.
ii. THERE MUST BE A CLEAR RULE THAT DESCRIBES
THE RELATION.
iii. THERE IS A DIRECTIONAL PROPERTY.
𝑋: 1, 2, 3, 4
𝑌: 2, 4, 6, 8
𝑋 → 2𝑋
𝑥 = 1 → 2𝑥 = 2
𝑥 = 2 → 2𝑥 = 4
𝑥 = 3 → 2𝑥 = 6
𝑥 = 4 → 2𝑥 = 8
1
2
3
4
2
4
6
8
X Y
• INPUT
• DOMAIN
• OUTPUT
• RANGE
3. TYPES OF RELATION
ONE TO MANY
If an element of a domain is mapped
onto more than one element of the
codomain (range).
MANY TO ONE
If two or more elements of the domain
have the same image in the codomain.
ONE-TO-ONE
If no elements of the domain have the
same image in the codomain.
1
3
5
2
3
4
5
6
1
2
3
4
5
D
E
F
1
4
9
16
1
2
3
4
X Y X Y X Y
5. FUNCTIONS
SET OF ORDERED PAIRS
𝑋 = 𝑋1, 𝑋2, 𝑋3 , 𝑋4
𝑌 = 𝑌1, 𝑌2, 𝑌3 , 𝑌4
TABLE OF VALUES
GRAPH
X 1 2 3
Y 2 4 6
MAPPING
EQUATION
𝑦 = 𝑓(𝑥)
6. EXAMPLES AND NON-EXAMPLES OF FUNCTION
ONE-TO-ONE
FUNCTION
ONE-TO-ONE
FUNCTION
MANY TO ONE
FUNCTION
RELATION BUT NOT A
FUNCTION
RELATION BUT NOT A
FUNCTION
1
2
3
4
D
B
C
A
3
4
5
2
4
6
9
15
16
25
1
2
3
a
b
c
d
9
4
16
4
3
2
1
-2
-3
-4
2
5
7
9
t
f
h
7. VERTICAL LINE TEST
A vertical line test is a vertical line drawn to test a graph if it is a function.
If it passes once, then it is a function.
If it passes twice or more, then it is a function.
8. LINEAR FUNCTION
A function 𝑓 is a linear function if 𝑓 𝑥 = 𝑚𝑥 + 𝑏, where ,𝑚 and 𝑏 are real numbers, and ,𝑚 and 𝑓(𝑥) are not
both equal to zero.
To sell more, the class needs to charge a lower price as indicated in the following table.
EXAMPLE:
Target No. of
Shirt Sales
Price per T-
shirt
500 ₱ 540
900 ₱ 460
1 300 ₱ 380
1 700 ₱ 300
2 100 ₱ 220
2 500 ₱ 140
𝑥1 = 500 ; 𝑥2 = 900
𝑦1 = 540 ; 𝑦2 = 460
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1 ; 𝑚 =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
𝑦 − 540 =
460 − 540
900 − 500
= −
80
400
= −
1
5
𝑥 − 500
𝑦 − 540 = −
1
5
𝑥 − 500
𝑦 − 540 = −
𝑥
5
+ 100
𝑦 − 540 + 540 = −
𝑥
5
+ 100 + 540
𝑦 = −
𝑥
5
+ 640
𝑦 = −0.2𝑥 + 640
500, 540 𝑎𝑛𝑑 900, 460
Try the
function
and see if it
fits the
given data
in the table.
9. QUADRATIC FUNCTION
A quadratic function is any equation of the form 𝑓 𝑥 = 𝑎𝑥2
+ 𝑏𝑥 + 𝑐 where 𝑎, 𝑏, and 𝑐 are real numbers
𝑎 ≠ 0.
10. PLAN FOR PRODUCT LAUNCH
PLANNING
Synergize
scalable e-
commerce
MARKETING
Disseminate
standardized
metrics
DESIGN
Coordinate
e-business
applications
STRATEGY
Foster
holistically
superior
methodologies
LAUNCH
Deploy
strategic
networks with
compelling
e-business
needs
11. TIMELINE
SEP
2 0 X X
Synergize scalable
e-commerce
NOV
2 0 X X
Disseminate standardized
metrics
JAN
2 0 X X
Coordinate e-business applications
MAR
2 0 X X
Foster holistically superior
methodologies
MAY
2 0 X X
Deploy strategic networks with
compelling e-business needs
12. AREAS OF FOCUS
B2B MARKET SCENARIOS
• Develop winning strategies to keep ahead of the competition
• Capitalize on low-hanging fruit to identify a ballpark value
• Visualize customer directed convergence
CLOUD-BASED OPPORTUNITIES
• Iterative approaches to corporate strategy
• Establish a management framework from the inside
13. HOW WE GET THERE
ROI
• Envision multimedia-based expertise
and cross-media growth strategies
• Visualize quality intellectual capital
• Engage worldwide methodologies
with web-enabled technologies
NICHE MARKETS
• Pursue scalable customer service
through sustainable strategies
• Engage top-line web services
with cutting-edge deliverables
SUPPLY CHAINS
• Cultivate one-to-one customer
service with robust ideas
• Maximize timely deliverables for
real-time schemas
14. SUMMARY
At Contoso, we believe in giving 110%. By using our
next-generation data architecture, we help
organizations virtually manage agile workflows. We
thrive because of our market knowledge and great
team behind our product. As our CEO says,
"Efficiencies will come from proactively transforming
how we do business."
