Name: Period: Score: First attempt due: Final score: Math Journal: Final corrections due: Inverse Functions in

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 . For the 2014 contest, there are three players from East conference (Paul George, Terrence Ross, and ) and three more from West conference (, , 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 2 person's height, in feet, can be modeled by 푓(푥) = 푥 + 1 where x is the person's standing reach, in feet. 3

1. Paul George has a standing reach of 8.5 feet. Find his height; round your answer to the nearest tenth of a foot. Show your work. Record your answer in the table on the back.

푓(8.5) =

2. Find the inverse of 푓(푥) and simplify completely. Show your work.

3. Harrison Barnes is 6.7 feet tall. Find his reach using your equation for 푓−1(푥); round your answer to the nearest tenth of a foot. Show your work. Record your answer in the table on the back.

푓−1(6.7) =

672−푥2 The standing reach, g(x) (in feet) is given by the function 푔(푥) = where x is the person's jumping velocity in feet 64 per second.

4. Ben McLemore has a jumping velocity of 12.4 feet per second. Find his standing reach; round your answer to the nearest tenth of a foot. Show your work. Record your answer in the table on the back.

푔(12.43) =

672−푥2 푔(푥) = finds a person’s standing reach given their jumping velocity, x in feet per second. The inverse of the 64 function is 푔−1(푥) = √672 − 64푥 , which finds the person’s jumping velocity given their standing reach in feet. 5. Damian Lillard has a standing reach of 7.9 feet. Find his jumping velocity using the inverse equation above; round your answer to the nearest tenth of a foot per second. Show your work. Record your answer in the table below.

푔−1(7.9) =

6. Use the equations 푓(푥), 푓−1(푥), 푔(푥), and 푔−1(푥) from above to find the rest of the missing information in the table below. Show work in each box or attach a separate sheet.

Jumping Height Standing reach Player Team velocity (feet) (feet) (feet per sec)

Harrison Barnes Golden State 6.7 ft

Damian Lillard Portland 7.9 ft

Western

Ben McLemore Sacramento 12.4 ft/sec

Paul George Indiana 8.5 ft

Terrence Ross Toronto 6.5 ft

Eastern

John Wall Washington 12.7 ft/sec

7. Based on the information you compiled, which conference do you think won the 2014 Slam Dunk Contest? Explain your reasoning.