indicates that a student should be able to complete this item without a

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1 The semester A eamination for Honors Algebra will consist of two parts. Part 1 will be selected response on which a calculator will NOT be allowed. Part will be short answer on which a calculator will be allowed. The symbol calculator. indicates that a student should be able to complete this item without a If a calculator is used to find points on a graph, the appropriate calculator function (i.e., zero, intersect, minimum, or maimum) should be used. The trace function should not be used. Decimal approimations must be correct to three places after the decimal point. Unless otherwise specified, the domain of any function is assumed to be the set of real numbers for which the function rule returns a real number. The symbol represents the greatest integer function. No formulas will be provided in the eamination booklet. 1. Sketch the graph of f 1, if 0 4, if 0 For items and, write the functions represented by the graphs below... y y MCPS

2 4. When ordering items from a catalog, the buyer has the option of having items giftwrapped. The shipping charge for every order is $1.00. In addition, if 5 items or less are gift wrapped, the charge is $5.00 per item gift-wrapped. If more than 5 items but less than 10 items are gift-wrapped, the charge is $4.50 per item gift-wrapped. If 10 or more items are gift-wrapped, the charge is $.00 per item gift-wrapped. a. Write a piece-wise function for the total charge of gift-wrapping items, including the shipping charge. b. If the total charge plus shipping was $51.00, how many items were gift-wrapped? 5. Let f 4. a. Sketch the graph of f. b. What is the domain of f? c. What is the range of f? d. What is the verte of the graph of f? e. What is the equation of the ais of symmetry of the graph of f? f. What is the minimum value of f? g. Is the function f continuous? For items 6 through 1, use the following functions: f g 8 h For items 6 and 7, evaluate. 6. f g 7. h f 7 For items 8 through 1, perform the indicated operation. 8. f g 9. f g MCPS 01 01

3 10. f g 11. f g 11b. What is the domain of f g? 1. gh 1. h f 14. If f 16 and g a. What is the domain of f g? b. What is the domain of g f? For items 15 through 18, state whether or not the function is one-to-one. 15. f f 17. f 18. f Are f 7 6 and g 6 inverse functions? Verify your answer algebraically If f 5, which of the following represents the inverse function f? A B C D f f f 5 1 f 15 MCPS 01 01

4 1 1. If g9 10, determine the inverse function, g. If yis, a point on the graph of a function corresponding point on the graph of the function f., what are the coordinates of a For items and 4, for each function graphed below, sketch the inverse function. f 1? Let f 4. What modification of the domain of f 1 f, being a function? For items 6 and 7, let f. Describe the transformations of f the graphs of the following functions. 6. g 1 7. h5 9 results in its inverse that will produce 8. The graph of a function f is to be transformed to create three new functions. Write the rule for each function in terms of f for the following. a. The graph of f is reflected about the -ais and stretched horizontally by a factor of three to create g. g b. The graph of f is reflected about the y-ais and translated down five units to create the graph of h. h MCPS

5 c. The graph of f is stretched vertically by a factor of si, then translated to the left seven units to create the graph of j. j For items 9 through 4, use the following matrices. A 4 5 B C D What are the dimensions of the product matri BD? A 5 B 5 C 5 D 5 0. Suppose there eists a matri E such that the product matri BE has rows and 7 columns. What are the dimensions of matri E? 1. If 44 y 4 AB , what is the value of y?. Determine the value of in matri C such that AC For what value of is the determinant of matri C equal to 15? 4. For what value of will matri C not have an inverse matri? A 6 B 0 C 6 D Matri C will have an inverse matri for every value of. MCPS

6 5. Barry s Burgers offers three different types of burgers at three different prices. The types are the Hamburger, the Cheeseburger, and the BarryBurger. Jill and her friends visited Barry s Burgers three times. The first time, Hamburgers, 5 Cheeseburgers, and 6 BarryBurgers cost $5.4. The second time Hamburgers, 7 Cheeseburgers, and 5 BarryBurgers cost $5.68. The third time, 4 Hamburgers, 4 Cheeseburgers, and 7 Barryburgers cost $6.59. a. Write a system of equations that represents this situation. Be sure to define the variables. b. Represent the system as a matri equation. c. Determine the cost of each type of burger. 6. The volume of a gift bo is given by the function V h 4h h 60h, where h represents the height of the bo, with domain 0h. What is the height of the bo with the maimum volume? 7. Write the comple number represented by points A-E on thegraph below. imaginary B C A real E D MCPS

7 8. Identify each of the following as real, pure, imaginary, and/or comple. a. b. 9 c. 5 i For items 9 through 46, perform the indicated operations. 9. i5 7i i1 i 41. 8i8 i 4. 7i i i 7i 1 6i 45. i i For items 47 and 48, fill in the blank with the number that will complete the trinomial square Describe the relationship between the discriminant (zeros) of the quadratic equation a b c 0. b 4acand the nature of the roots For items 50 and 51, solve for all values of MCPS

8 For items 5a through 5 c, grid in and bubble your answers in the grids provided. 5. An arrow is shot from a height of feet with an initial velocity of 56 feet per second. The equation for the height, in feet of the arrow at time t (in seconds) is ht 16t 56t. a. After how many seconds will the arrow hit the ground? b. How many feet high will the arrow be at t 1.5 seconds? c. What is the maimum height, in feet, that the arrow will reach? 5a. 5b. 5c. / / / / / / If f, on what interval of -values is f decreasing? MCPS

9 54. What are the left- and right-end behaviors of the function f 4 8? As, As f f, What are the left- and right-end behaviors of the function f 4 4? As, As f f, n n1 56. A polynomial function has a general form of a n an 1... a 1 a0, where n is a positive integer. Describe the left- and right-end behaviors for the following values of an and n. a. an is positive, n is even. As, As n f n f, b. an is positive, n is odd. As, As n f n f, c. an is negative, n is even. As, As n f n f, d. an is negative, n is odd. As, As n f n f, For items 57 and 58, write an equation in factored form for the graphs shown below MCPS

10 For items 59 and 60, factor For items 61 and 6, find all zeros of each function. Show how you determined your zeros. 61. f f Write a polynomial function with real coefficients in factored form if two of its comple zeros are and 9i. 64. Write a polynomial function with real coefficients in factored form if two of its comple zeros are 8,7 i, and 5i. 65. Determine if each epression below is a factor of each epression Write yes or no for a. b. 6 c. 5 d. e. f Divide Given f. a. Find the zeros of the function and sketch the graph. b. Complete: As f, c. Complete: As f Let f, Determine if each number below is a possible rational root (zero) according to the rational root theorem. Write yes or no for each number. a. 5 b. 1 c. 4 d. 4 e Using the rational root (zero) theorem, list the possible rational roots (zeros) of 4 f MCPS

11 70. A fourth degree polynomial with real coefficients could have how many imaginary roots? 71. Let 4 f 4. a. How many zeros does this function have? b. How many real zeros does this function have? 7. Let 5 f 4 a. How many zeros does f have? A 0 B 1 C 4 D 5 b. How many real number zeros does f have? A 0 B 1 C 4 D 5 7. Solve the inequality Look at the graph of f 115below. Solve the inequality MCPS

12 75. The solutions of are 6, 1,and 8. a. Write the polynomial in factored form. b. Solve the inequality algebraically. 76. The solutions of are 4,,and 7. a. Write the polynomial in factored form. b. Solve the inequality algebraically. 77. Solve the inequality Complete the chart. Any decimal approimations should be accurate to three decimal places. Function f g Value(s) of any local maimums Value(s) of local minimums Interval(s) where the function is increasing Interval(s) where the function is decreasing 79. Sam throws a ball from the top of a building. The table below shows the height of the ball above the ground. Time (sec) t Height (ft.) f t a. Write a polynomial function that best fits the data. b. High how is the ball after 4 seconds? c. When does the ball hit the ground? MCPS

13 For items 80 and 81; a. Determine the degree of the polynomial that models the data. b. Use the regression feature on your calculator to write a function that models the data f f Write the equation in verte form, y ah k, for the parabola with verte, and passing through the point 7,8. 8. Write the equation in verte form, y ah k, for the parabola with verte 1, 4 and passing through the point 5,5. MCPS