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FUNCTIONS AND RELATION.pptx
- 1. FUNCTIONS AND RELATIONS PREPARED BY:CINDY BONONO-CABARIBAN
- 2. RELATION i. TWO SETSARE 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 ONETO 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
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- 5. FUNCTIONS SET OFORDERED 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-EXAMPLESOF 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 Avertical 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 function𝑓 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 quadraticfunction is any equation of the form 𝑓 𝑥 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 where 𝑎, 𝑏, and 𝑐 are real numbers 𝑎 ≠ 0.
- 10. PLAN FOR PRODUCTLAUNCH 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 XX 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 B2BMARKET 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 GETTHERE 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, webelieve 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."
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