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Graph Systems of Linear Inequalities

Graph Systems of Linear Inequalities. Peter Paliwoda. Multi-step video game problem.

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Graph Systems of Linear Inequalities

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  1. Graph Systems of Linear Inequalities Peter Paliwoda

  2. Multi-step video game problem • An online media store is having a sale, as described in the ad shown. Use the information in the ad to write and graph a system of inequalities for the regular video game prices and possible sale prices. Then use the graph to estimate the range of possible sale prices for games that are regularly priced at $20. ONE DAY SALE! SAVE 30%-70% ON ALL VIDEO GAMES REGULAR PRICE: $20-$50)

  3. System of Inequalities • x>=20 Regular price must be at least $20 • x<=50 Regular price can be at most $50 • y>=0.3x Sale price is at least (100-70)%=30% of regular price • y<=0.7x Sale price is at most (100-30)%=70% of regular price ONE DAY SALE! SAVE 30%-70% ON ALL VIDEO GAMES REGULAR PRICE: $20-$50)

  4. Graph Inequalities y x>=20 x<=50 Sale Price (dollars) y<=0.7x y>=0.3x x Regular Price (dollars)

  5. Identify the Range of Possible Sale Prices • From the graph you can see that when x=$40, the value of y is between these values: 0.3(40)=12 and 0.7(40)=28 So, the value of y satisfies 12 <= y <= 28

  6. Modeling Bicycle • Speed of a Bicycle: The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches respectively. A cyclist is pedaling at a rate of 1 revolution per second.

  7. Find Speed of Bicycle in ft/min

  8. Write function for Distance d (in miles) in terms of n revolutions of the pedal

  9. Write a function for the distance d (in miles) a cyclist travels in terms of time (in seconds).

  10. Why should you learn Inverse functions • It is useful in manipulating graphs and the way they are displayed • Recall that to find the inverse of a line of points f(x)={(1,5),(2,6),(3,7),(4,8)} is done by interchanging the first and second coordinate • f-1(x)={(5,1),(6,2),(7,3),(8,4)} • So, f is equal to the range of f-1 and vice versa.

  11. Problem • The factory sales f (in millions of dollars) of digital cameras in the United States from 1998 to 2003 are shown in the table.

  12. Questions • Does f-1 exist? • If f-1 exists, what does it represent in the context of the problem? • If f-1 exists, find f-1 (1825) • If the table was extended to year 2004 and if the factory sales of digital cameras for that year was $2794 million, would f-1 exist? Explain

  13. Does f-1 exist? Yes, it does exist! f(x) f-1(x)

  14. If f-1 exists, what does it represent in the context of the problem? • f-1 represents the domain of f in f(x) in f-1(x)

  15. If f-1 exists, find f-1 (1825) f-1(x)

  16. If the table was extended to year 2004 and if the factory sales of digital cameras for that year was $2794 million, would f-1 exist? Explain • No, because the extended function would fails the horizontal line test. More than one horizontal intersection

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