Final Exam Review Spring 01-013 Name Module 4 Fill in the charts below. x x -6 0 Change in 0 0 Change in -3 1 1-1 4 5 0 9 3 10 16 4 17 5 5 5 6 6 36 6 37 1 Is this a quadratic? Is this a quadratic? b. EXPLAIN wh or wh not. b. EXPLAIN wh or wh not!! For numbers 3-6, find each of the following: A: Calculate and state whether the function has positive or negative concavit. B: Explain how ou know and show all work. C: Identif the vertex and axis of smmetr. 3. 6x 11x 10 4. = 3(x-)(x+4) 5. ( x 3) 8 6. x 18x 8 7. A baseball plaer pops a fl ball straight up. The ball reaches a height of 68 feet before falling back down. Roughl 4 seconds after it is hit, the ball lands in left field. The graph below shows the height of the ball over time. 100 90 ) b.) c.) When is the ball 68 feet high? How man times will it be 40 feet high? What is the height of the ball after 1 second? 80 70 60 50 40 30 0 10 1 3 4 5 x
8. A water balloon is dropped from the top of a tall building. The water balloon s height in meters, (t) seconds after it is dropped is h(t) = -4.9t + 70 Find h(3) and give a real-world meaning for this value. b. How tall is the building? c.when will the water balloon be 15 meters above the ground? Estimate. 9. A small rocket is fired into the air from the ground. It s trajector can be modeled with the equation h = -.5t + 5t where h is the rocket s height after t seconds. How long does it take for the rocket to reach its high point? b. Find the rocket s maximum height during its flight. c. How man seconds does it take for the rocket to return to the ground? 10. A basketball plaer shoots at a basket that is 10 feet from the floor. The function d 16t 0t 6 gives the distance from the ball to the floor in feet. Explain how the equation 10 16t 0t 6 can help ou find where the ball is at the basket level. b. Solve the equation in part Which solution represents the time that the basketball passes through the basket? c. Given the equation 0 16t 0t 6, solve for t and explain the real world meaning of the solution. d. Which of the solution in part c makes sense? Explain. For numbers 11-13, find the roots, vertex and axis of smmetr for the following: 11. g(x) = (x 3)(x + 4) 1. f(x) = -(5x + 3)(6 x 5) 13 b. 5 4 3 1 (, 0) (6, 0) 7 6 5 4 3 1 1 3 4 5 6 7 x 1 3 5 4 3 1 5, 0) ( 1, 0) 5 4 3 1 1 3 4 5 x 1 3 4 5 (0, 4) 4 5 (0, 5)
For numbers 14 19, the quadratic functions are given in standard form, find the following: Write in factored form. b. State the zeros of the function. c. Find the -intercept. 14. ( ) 81x f x 64 15. g ( x) 3x 6 16. h ( x) x 8x 15 17. f ( x) 6x 7 x 15 18. 0 x 11x 0 19. 18 x x 10 0. Given the function f ( x) ( x 3), state the vertex b. write the function in standard form c. find the -intercept. 1. Given the function k ( x) 1 x 7, find the vertex form b. state the vertex c. find the -intercept For questions -3, use the quadratic formula to find the roots. State the answers in decimal form and round to the nearest hundredth.. h ( x) 9x 4 x 16 3. f ( x) 5x 13x 7 Rewrite the following expressions as in imaginar number. 4. 99 5. 4 Rewrite each quadratic function with imaginar numbers as zeros in standard form. 6. f x ( x i)( x 3i) 7. g( x) 3( x 4i)( x 4i) For numbers 8-30, find the zeros of the following quadratics. Write the imaginar roots as complex numbers in standard form. 8. f ( x) 5x 1 9. ( ) 4x g x 53 30. h ( x) x
Chapter 3 1. Use the Leading Coefficient Test to determine the end behavior of the graph of the given polnomial function. f(x) = -x 4 + x b. f(x) = x 3 4x c. f(x) = (x 3) d. f(x) = -x 3 x + 5x - 3. Find the zeros for each polnomial function and give the multiplicit for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x) = 3(x + 5)(x + ) b. f(x) = 4(x 3)(x+ 6) 3 3. For each function, i. Use the Leading Coefficient Test to determine the graph s end behavior. ii. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. iii. Find the -intercept. iv. Find a few additional points and graph, the function. Use the maximum number of turning points to check whether it is draw correctl. f(x) = x 3 + x x b. f(x) = x 4 x 3 + x 4. Divide using long division. (6x 3 + 7x + 1x 5) (3x 1) b. 5. Divide using snthetic division. (x 5x 5x 3 + x 4 ) (5 + x) b. 6. Use snthetic division and the Remainder Theorem to find the indicated function value. f(x) = x 3 11x + 7x 5; f(4) 7. Solve the equation x 3 5x + x + = 0 given that is a zero of f(x) = x 3 5x + x +. 8. Use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = 3x 4 11x 3 x + 19x + 6 b. f(x) = x 5 x 4 7x 3 + 7x 1x 1 9. Given f(x) = x 3 3x 11x + 6 List all possible rational zeros. b. Use snthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining zeros of the polnomial function.
10. Given f(x) = 6x 3 + 5x 4x + 5 = 0 List all possible rational roots. b. Use snthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots of the polnomial function. 11. Find the domain of each rational function. ( ) ( )( ) 1. Find the vertical asmptotes, if an, of the graph of each rational function. ( ) ( ) ( ) 13. Find the horizontal asmptotes, if an, of the graph of each rational function. ( ) c. ( ) 14. Use transformations of ( ) or ( ) to graph each rational function. ( ) 15. Follow the seven steps to graph the rational function. ( ) 4x f ( x) x 16. Find the slant asmptotes of the graph of the rational function and follow the seven step strateg and x use the slant asmptote to graph each rational function f ( x ) x 6 x 3 17. Solve each polnomial inequalit and graph the solution set on a real number line. Express each solution set in interval notation. (x 4)(x + )> 0 b. 3 x + 10x 8 0 c. x 3 9x 7 0 18. Solve each rational inequalit and graph the solution set on a real number line. Express each solution set in interval notation. x 4 0 x 3 x b. 0 x 4
Module 5 1. Bigtown has an initial population of 5000 people and grows b 1% ever ear. Write a function to describe the amount of people in the town after an amount of ears.. Given f x 34 1. 08 x find: The growth factor b. The percent change c. The initial value 3. Given that the table shows exponential deca, find the following information. x 1 3 f(x) 51.94 7.58 14.5899 What is the deca factor? b. What is the percent change? c. What is the initial value? d. Write a function to describe this relationship. 4 3 1 6 4. Simplif 6a b c 5a b c. 5. A certain bacteria grows 1 % ever 8 minutes. Initiall, there was 30 micrograms of this bacteri What is the 8 minute growth factor? b. Write a function to determine the amount of bacteria after n 8 minute intervals. c. What is the 1 minute growth factor? d. Write a function to determine the amount of bacteria after t minutes. e. What will the mass of the bacteria be after 35 minutes? f. When will the bacteria s mass be 400 micrograms? 6. Given the equation 4 t h t 943.5, where t is in das, answer the following questions. 4 da growth factor: b. 1 da growth factor: c. 1 da percent change: 7. Write a function for a bank account that has an advertised 4.3% APR, compounded quarterl, if $300 is invested initiall. Leave our answer in terms of t. 8. For the above problem, how much mone will the account have after 8 ears? 9. Write a function for a CD in each situation, if $500 is invested initiall. 4.6% APR compounded quarterl. b. 4.5% APR compounded semiannuall. c. 4.3% APR compounded monthl. 10. Determine how much mone ou would have in each account after 0 ears.
11. How much mone would ou need to invest into an account offering 3% APR compounded monthl if ou wanted to have $10,000 after 10 ears? 1. Sasha invested $450 in an account that offered 3.76% APR compounded quarterl. What is the quarterl growth factor? b. What is the quarterl percent change? c. What is the annual growth factor? d. What is the annual percent change? 13. Write each in logarithmic form. b. c. 14. Write each in exponential form. b. c. 15. Condense and simplif. No calculator. b. c. 16. Rewrite each of the following as sums and differences of a logarithm of some number. ( ) 17. Solve the following, and round to three decimal places. 18. Solve the equation.035 100 700 1 1 1x, rounding our answer to three decimal places. 19. Adam invests $3000 at an interest rate of.4% compounded monthl, while Brenda invests $3500 at an interest rate of.5% compounded semiannuall. Who will have more mone after 15 ears? How much mone will each person have after 15 ears?