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CC Coordinate Algebra Unit 3b Test Review – Day 42 Name: _________________________________________ Date: _____________________________ Characteristics of Functions: For each of the functions find the following information. 1. 2. Domain: ___________________ Range: ___________________ x - intercept: _______________ y- intercept: __________________ Increasing: ____________________ Decreasing: ____________________ Max / Min: ___________________ End Behavior: _x∞,y__ x-∞,y__ Rate of change over [-1, 2] ____ Domain: ____________________ Range: _______________________ x - intercept:__________________ y- intercept: __________________ Increasing: ______________________ Decreasing: _____________________ Max / Min: _____________________ End Behavior: __ x∞,y__ x-∞,y__ Rate of change over [-1, 2] ___ 3. Discuss and compare the functions by analyzing the rates of change, intercepts, and where one function is greater or less than the other. Combining Functions Given the functions: f ( x) 3x 2 2 x 6 , g ( x) 4 x 2 x 8 4. Find f(2) ___________ 5. Find f(-2) + g(3) __________ 6. Find f(x) – g(x) __________ 7. Find 2f(x) + 4g(x). ____________ Linear and Exponential Models: 8. Write an explicit and recursive formula to model the number of dots per day. Day 1 Day 2 Day 3 CC Coordinate Algebra Unit 3b Test Review – Day 42 9. Sherry has a huge doll collection of 80 dolls. Her mom tells her that she needs to get rid of 5 per year to get it down to a decent number before leaving for college. Write an explicit and recursive formula to model the number of dolls per day. If she is 12, how many will she have left when she is 18? 10. You bought a Boston Whaler in 2004 for $12,500. The boat’s value depreciates by 7% a year. How much is the boat worth now? How much is it worth in 2020? 11. The population of a large city increases by a rate of 3% a year. When the 2000 census was taken, the population was 1.2 million. a) Write a model for this population growth. b) What should the population be now? What is the projected population for 2020? 12. Bank Plans: Suppose you worked mowing lawns all summer and earned $100. Two savings institutions want you to let them “hold onto your money” for a while. Linear Luck: This savings plan will add $100 to your balance for every month that you leave your money in the account. Exponential Experiment: This savings plan will multiply your balance by 2 every month that you leave your money in their account. Analyze the plans: Write the explicit function for each account, and decide which account is best at what times. Transformations: 13. Describe the transformations made to f(x) = 2x to draw the following functions. a) g ( x) 1 3x 2 5 4 b) h( x) 2(3) x 1 1 14. Give the domain, range, and asymptote for g ( x) 3x 2 5 . 4 15. Sketch the graph of -f(x)+2. 16. Sketch the graph of 2f(x)-1. CC Coordinate Algebra Unit 3b Sequences: 16. Given the recursive formula A1 = 4; An = An-1(3), what is A5? 17. Given the explicit formula An = 5(-3)n-1, find the 6th term. 18. If An= An-1 +12 and A10= 2, what is A15? Even and Odd Functions 19. Is the equation f(x) = 2x2 + 6 even, odd or neither? Why? 20. Is the equation g(x) = -6x5 + 5x even, odd or neither? Why? 21. Is the graph of the function even, odd or neither? Why? 22. Is the graph of the function even, odd or neither? Why? Test Review – Day 42