Name: Period: Date: Math Journal: Inverse Functions in Basketball
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Name: Period: Date: Math Journal: Inverse Functions in Basketball Every year the NBA holds an All-Star game. During the weekend of the All-Star game, other competitions are put on by the NBA, such as the slam dunk contest. For the 2014 contest, there are three players from East conference (Paul George, Terrence Ross, and John Wall) and three more from West conference (Harrison Barnes, Damian Lillard, and Ben McLemore). These players will complete in two rounds. In the Freestyle Round, the three dunkers for each conference will have a 90 second limit to make as many dunks as they want, in the order they want and assisting each other if necessary. Each player has to make at least one dunk. The panel of judges will determine which conference wins the Freestyle Round. The Battle Round will consist of head-to-head matchups (East dunkers vs. the West dunkers). The conference that won Freestyle Round will be given the choice of order for dunks in the Battle Round. Each player will be limited to three attempts to complete a Battle Round dunk. Upon losing a head-to- head battle, the losing dunker is eliminated from the competition. The first conference to win three head- to-head battles will win the Battle Round and be crowned Slam Dunk champions. A basketball hoop is 10 feet above the floor. A player must jump high enough to reach 10.5 ft. to make a slam dunk. A person's height h in feet can be modeled by where r is the person's standing reach in feet. The initial velocity v (in feet per second) at which a person must jump to make a slam dunk is given by where r is the person's standing reach in feet. 1] Paul George has a standing reach of 8.5 feet. 2] Ben McLemore has a jumping velocity of Find his height. Show your work. 12.43 feet per second. Find his reach. Show your work. 3] Find the inverse of Show your work. 4] finds a person’s height given their standing reach. finds the person’s standing reach given their height. Which of the following is a way to rewrite in function notation: ? Rewrite with that notation. 5] Harrison Barnes is 6.7 feet tall. Find his reach. Show your work. 6] Find the inverse of Show your work. 7] finds a person’s standing reach given their jumping velocity. finds the person’s jumping velocity given their standing reach. Which of the following is a way to rewrite in function notation: Rewrite with that notation. 8] Damian Lillard has a standing reach of 7.9 feet. Find his jumping velocity. Show your work. 9] Find the composition . Show your 10] first finds a person’s standing work. reach given their jumping velocity, and then uses that standing reach to find the person’s height. Which of the following is a way to rewrite in function notation: Rewrite with that notation. 11] John Wall’s jumping velocity is 12.6 feet per second. Find his height. Show your work. 12] Find the inverse of Show your work. 13] finds a person’s height given their jumping velocity. finds the person’s jumping velocity given their height. Which of the following is a way to rewrite in function notation: Rewrite with that notation. 14] Terrence Ross is 6.5 feet tall. Find his jumping velocity. Show your work. 15] Use the solutions from the problems above to complete the table. Jumping Standing Height velocity Player Team reach (feet) (feet per (feet) second) Harrison Barnes Golden State 6.7 Damian Lillard Portland 7.9 Western Ben McLemore Sacramento 12.43 Paul George Indiana 8.5 Terrence Ross Toronto 6.5 Eastern John Wall Washington 12.65 16] Based on the information you compiled, which conference do you think will win the 2014 Slam Dunk Contest? Explain your reasoning. .