**This activity was developed by a
student or students at Mainland High School which is located in Daytona Beach, FL.
It is still a "work in progress" with editing and improvements yet to come.**

The students at Lima Middle School want to increase student participation in extracurricular activities noting that there has been a significant decrease in recent years accompanied by an increase in youth drug and alcohol usage. In this project, you will graph and analyze functions and transformations that model these trends.

Starting in 1990, the percent decrease follows the function

** f (t)= 35-2t** where

1. What percent of students participated in extracurricular activities in 1993? in 1995?

2. Assuming the trend continues, what percent of students will participate in the year 2000?

3. Use the grid provided to graph the function for a domain of all integers between 0 and 5 inclusive.

4. Give a function that would be symmetric to

35-2with respect to the vertical linet=5.t5. Assuming this function was put into effect in 1995, when would the percent of participants be greater than 50%?

6. Assuming the goal is to reach 50% participation by the year 2000, what linear function should be put in effect in 1995?

7. Use the grid provided to graph this function for integer values of t from 5 to 10 inclusive.8. Suppose the school has to delay the implementation of a corrective function until 1996 with a new goal of reaching 50% participation by the year 1999. What would the new linear function be?

One of the few areas where student participation has increased is in female athletics. The number of females participating in 1990 was 20 with the number increasing per year described by the function

for all integers.f(t) =3t^{2}+ 209. How many females participated in 1993? In 1995?

10. Use the grid provided to graph the function for a domain of all integers between 0 and 5 inclusive.11. Assuming there are 400 females in the school and this number remains constant, what quadratic function would describe the number of females who do nat participate in athletics?

In an attempt to accelerate the increase in in participation in female athletics, new intramural programs were introduced for 1993 in four sports.

12. If the level of participation in 1995 is 113 females and 176 in 1996, what quadratic function represents this trend?

13. Use the grid to graph this function for a domain of all integers between 2 and 7 inclusive.

14. What would be the number of participants in 1997?

This table summarizes participation in four other extracurricular activities between 1990 - 1995.

Year

t

Band

Spanish Club

Football

Spirit Club1990

0

105 30 45 79 1991 1 102 27 40 78 1992 2 93 24 35 76 1993 3 78 21 40 72 1994 4 57 18 45 64 1995 5 30 15 50 48

15. Give a function that describes band membership in terms of

.t16. What is the parent function for this function?

17. What transformations are associated with the band function?

18. Use the grid provided to graph the band function for a domain of all integers t between 0 and 5 inclusive.

19. What function models Spanish Club membership in terms of

?t20. What is the parent function for the Spanish Club membership function?

21. What transformations are associated with this function?

22. Use the grid to graph the Spanish Club function for a domain of all integers t between 0 and 5 inclusive.23. Give a function that models participation in football in terms

?t24. What is the parent function for this function?

25. What transformations are associated with the football function?

26. Use the grid provided to graph the football function for a domain of all integers t between 0 and 5 inclusive.

27. What function models Spirit Club membership in terms of t?

28. What is the parent function for this function?

29. What transformations are associated with the Spirit Club function?

30. Use the grid provided to graph the membership function for a domain of all integers t between 0 and 5 inclusive.

The function

wheref(x) = 200/x0 < x < 100describes the likelihood of drug or alcohol usage based on the percentage of students involved in extracurricular activities.31. What is the parent function?

32. What transformations have been performed on the percent function?

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