Alberta Distance Learning Centre MAT3791 Math 30-1 Unit 7: Baker Street Review Lesson B: Unit 3 and Unit 4 Review Student's Questions and Comments For Student use only For ADlC USE ONLY (If label is missing or incorrect) Assigned to File Number: Marked by Name Address Province Postal Code Apply Assignment Label Here City/Town Please use the correct preprinted label for this course and Assignment Booklet. Mark:\t% Date Received: Summary Total Weighting Practice SelfAssessment 20% Assignment 80% Blended Booklet Grade Teacher's Comments Teacher's Signature NEW SEPT 2012 Your Marks Mathematics 30-1: Unit 7 Lesson B - Assignment Booklet Back to Baker Street... Complete the Back to Baker Street assignment. Refer to the Tips from Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment. Please show pertinent work and explanations. Call or e-mail your teacher if you would like additional help. Multiple-Choice Items 1 2 1. Select the inverse of the following graph: A. B. D. C. 2. Identify the inverse equation of the function f^ xh = x+ 3 5 . A. f -1(x) = 3x + 5 B. f -1(x) = 5x - 3 C. f -1(x) = x - 15 D. f -1(x) = 5x + 15 Alberta Distance Learning Centre 39 Lesson B - Assignment Booklet Mathematics 30-1: Unit 7 Numeric Response 1 1 The point (-1,2) lies on y = f(x) and undergoes a vertical and horizontal stretch. The corresponding point on a transformed function is (-4,1); then, the vertical stretch factor is 4 3. Choose the correct description of how y = 2 3x - 12 can be produced from y = x . A. Vertical stretch by a factor of 3, horizontal stretch by a factor of 1 , 2 horizontal translation of 12 units right 1 B. Vertical stretch by a factor of 2, horizontal stretch by a factor of 3, horizontal translation of 4 units left C. Vertical stretch by a factor of 1 , horizontal stretch by a factor of 1 , 3 2 horizontal translation of 12 units left D. Vertical stretch by a factor of 2, horizontal stretch by a factor of 1 , 3 horizontal translation of 4 units right 4. Select the equation of the radical function that is a transformation of y = x , in the domain " x | x $ 2, x d R , with a vertical stretch by a factor of 3. A. y = 3 x - 2 1 y= x- 2 B. 3 y = 3 x+ 2 C. 1 y= x+ 2 D. 3 Numeric Response 2 1 40 The point (5,12) lies on the graph of y = g(x). If the function is transformed to the new function y = g(x - 6) + 7, a point on this new graph will be (n,19). The value of n is Alberta Distance Learning Centre Mathematics 30-1: Unit 7 2 5. The phase shift and vertical displacement of y = 2 sin(x + 30) + 3 when compared to y = sin(x) will be 2 Lesson B - Assignment Booklet A. phase shift of 30 to the right and vertical translation of 3 units down B. phase shift of 30 to the left and vertical translation 2 units up C. phase shift of 30 to the right and vertical translation of 2 units down D. phase shift of 30 to the left and vertical translation 3 units up 6. The range of the function f(x) = -2 cos(3(x - )) + 4 is 6 # f^ xh # 10 A. 2 # f^ xh # 6 B. - 10 # f^ xh # - 6 C. - 6 # f^ xh # - 2 D. Numeric Response 3 1 The point (-3,5) lies on y = f(x). This point maps onto the point (8,9) on a new function y = f(x - h) + k. The value of k is 2 7. The maximum value reached by the function f(x) = 3 cos(2x - ) + 4 is A. 4 B.\t3 C.\t7 D.\t6 Alberta Distance Learning Centre 41 Lesson B - Assignment Booklet 2 Mathematics 30-1: Unit 7 8. If you begin with y = 2 x and transform it to y = 3(2)4(x -1) + 5, the horizontal and vertical stretch factors are A. horizontal stretch factor of 1 and vertical stretch factor of 3 4 1 and vertical stretch factor of 4 B. horizontal stretch factor of 3 C. horizontal stretch factor of 1 and vertical stretch factor of 2 4 1 and vertical stretch factor of 4 D. horizontal stretch factor of 2 Numeric Response 4 4 r A sinusoidal function, y = a sin(b(x - c)) + d has a maximum point at ` 8 , 3 j and a 3r subsequent minimum point at ` 8 , - 1 j . The values, in this order, of a, b, c and d are 2 3 - 5 are 9. The horizontal and vertical asymptotes of y = ^ x - 2h 2 A. horizontal asymptote of x = -2, vertical asymptote of y = 5 B. horizontal asymptote of x = 2, vertical asymptote of y = -5 C. horizontal asymptote of y = 5, vertical asymptote of x = -2 D. horizontal asymptote of y = -5, vertical asymptote of x = 2 10. The domain of y = 5f^2x + 4h + 3 where f^ xh = 1 is x A. x -4 B. x -2 C. x0 D. x -3 42 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 3 Lesson B - Assignment Booklet t 11. The equivalent equation to y = 2.5^2h5 is A. t = 5 log2 ` y j 2.5 B. t = log2(2y) C. t = 5log5(y) D. t = log2(5y) 2 12. The inverse function, y = f - 1(x), of f(x) = 2-x + 1 has A. domain of x > 0 and no x-intercept B. domain of x > 1 and no x-intercept C. domain of x > 1 and an x-intercept of 2 D. domain of x > 0 and an x-intercept of 2 Numeric Response 5 2 The value of n, to the nearest hundredth, if log8(32) = 2n, is 1 13. The logarithmic function, y = logb(x), has been transformed. The transformed function which does not have a change in the domain is A. y = 2f(x) + 3 B y = 2f(x - 4) + 3 C. y = f(x + 4) + 3 D. y = 2f(-x) - 4 Alberta Distance Learning Centre 43 Lesson B - Assignment Booklet 3 Mathematics 30-1: Unit 7 14. The function f(x) = logb(x) has been transformed to g(x) = -2logb(x + 3). The graph of g(x) could be found by A. translating f(x) 3 units to the left, reflecting the graph in the x-axis, and then stretching the graph vertically by a factor of 2 B. reflecting f(x) in the x-axis, translating the graph 3 units to the left, and then stretching the graph vertically by a factor of 2 C. reflecting f(x) in the y-axis, stretching f(x) vertically by a factor of 2, and then translating the graph 3 units to the left D. reflecting f(x) in the x-axis, stretching f(x) vertically by a factor of 2, and then translating the graph 3 units to the left Numeric Response 6 2 The x-intercept of the graph of f(x) = log5(x) is 1. The x-intercept, to the nearest hundredth, of the transformed function y = 4f(3 - x) + 2 will be: 4 15. The expansion of the logarithmic expression 2log4(16xy2) is 3 A. 4 + log4 x2 + log4 y4 B.\t4log4 16xy C.\tlog4 162 + 2log4 xy4 D.\tlog4 162 + log4 x4 + log4 y4 16. The logarithmic expression 3log2 x - log2(2y) + 3 can be written as A. log2 c x3 m + 3 y2 3x 3 m B. log2 c 2y x3 log2 c m C. 4y 4x3 m log2 c D. y 44 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 3 Lesson B - Assignment Booklet 17. The value of 2log3(4) - 2log3(12) is A. 2 B.\t-2 1 C. 9 2 D. 3 Numeric Response 7 4 If log4(x) = 12, then the value of log4(2x2) is 2 18. The solution to the equation log(10) - log(x) = 2log(x) is A. 8 B. 2 16 C. 3 3 D. 10 2 19. The exact solution to the equation 42x - 3 = 7x + 1 is log 7 - 3 log 4 A. x = 2 ^log 4 + log 7h log 7 - 3 log 4 x= B. 2 log 4 + log 7 log 7 + 3 log 4 x= C. 2 log 4 - log 7 log 7 + 3 log 4 D. x= 2 ^log 4 - log 7h Alberta Distance Learning Centre 45 Lesson B - Assignment Booklet 4 Mathematics 30-1: Unit 7 20. The solution to the equation logx(x + 3) - logx2 = 2 is A. -1 B.\t1 C. - 3 2 3 D. 2 Numeric Response 8 4 If the rate of growth in the number of fruit flies in an controlled environment is 10%/ hour, the number of hours, to the nearest hundredth, for the population to double will be Written Response 1. Assume you are given the function f(x) = 4(x - 1). 2 a. Determine the equation of the inverse of this function. 2 b. Sketch the graph of the function and its inverse on the grid below. 46 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 Lesson B - Assignment Booklet c. Determine the invariant point. Explain where invariant points will always occur in inverse relations and explain why. 2. You are given a sinusoidal function that passes through (0, 2), has a maximum point at (20, 5) and a minimum point at (60,-1) 3 a. Determine the amplitude, period and range of this function. 2 b. Determine a possible sine function with these characteristics. 2 c. Determine a possible cosine function with these same characteristics. 3. The function f(x) = logb(x + 2), passes through the point (14,2). 2 a. Determine the value of b. 2 b. Determine the value of n if this function passes through the point (n, 3). 2 c. Determine the value of m if this function passes through the point (6, m). 4 Alberta Distance Learning Centre 47 Lesson B - Assignment Booklet Mathematics 30-1: Unit 7 4. When comparing the sound measured in decibels, a normal conversation between two people measured 60 dB while the threshold of pain from loud noise is often considered to be 130 dB. The formula used to calculate sound in decibels I is b = 10 log c m , where is the dB reading, I is the intensity of the sound and I0 W I0 = 10 -12 2 . m 2 a. Determine how many times louder the intensity of the threshold of pain is compared to the conversation. 2 b. If the conversation intensity was tripled, determine what the new decibel level would be. 5. Assume that $5000 can be invested at a rate of 5%/a compounded monthly. 2 a. Determine the value of the investment after 6 years. 4 b. Determine the length of time, to the nearest year, required for the investment to triple in value. Total: 48 97 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 Lesson B - Assignment Booklet S Standard of Excellence Students need to make connections to other courses to complete. Successful completion shows an ability to think beyond given examples. O Over the acceptable level of understanding Students need to make connections from within the course notes and example to complete. Successful completion shows an ability to draw from given instruction and apply skills to new problems. L Level of acceptable standards Students need to show acceptable levels of understanding to complete. Successful completion shows ability to follow given examples. V Below level of acceptable standards Student's response to question is below acceptable standard. E Inadequate level of acceptable understanding Student's response to question indicates student needs assistance in understanding basic concepts. Thinkstock Alberta Distance Learning Centre 49 Alberta Distance Learning Centre MAT3791 Math 30-1 Unit 7: Baker Street Review Lesson C: Unit 5 and Unit 6 Review Student's Questions and Comments For Student use only For ADlC USE ONLY (If label is missing or incorrect) Assigned to File Number: Marked by Name Address Province Postal Code Apply Assignment Label Here City/Town Please use the correct preprinted label for this course and Assignment Booklet. Mark:\t% Date Received: Summary Total Weighting Practice SelfAssessment 20% Assignment 80% Blended Booklet Grade Teacher's Comments Teacher's Signature NEW SEPT 2012 Your Marks Lesson C - Assignment Booklet Mathematics 30-1: Unit 7 Back to Baker Street... Complete the Back to Baker Street assignment. Refer to the Tips from Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment. Please show pertinent work and explanations. Call or e-mail your teacher if you would like additional help. Multiple-Choice Items 1 2 2 1. Select the statement that is false. A.\tif h(x) = f(x) + g(x), then g(x) = f(x) - h(x) B.\tif h(x) = g(x) + g(x), then 2g(x) = h(x) C.\tif f(x) + g(x) = h(x), then g(x) = h(x) - f(x) D. if f(x) - g(x) = h(x), then g(x) = f(x) - h(x) 2.\tGiven f(x) = -2x2 + 3x and g(x) = 1 - x2, then f(x) - g(x) = A.\t-3x2 + 3x + 1 B.\t-x2 + 3x - 1 C\t-3x2 + 3x - 1 D.\t-x2 + 3x + 1 3. Two functions f^ xh = x2 - 1 and g^ xh = x2 are added to find h(x). The range of the function h(x) is ydR A. y$1 B. C y $ 0 -1 $ y $ 1 D. 20 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 Lesson C - Assignment Booklet Numeric Response 1 3 If you are given the function g(x) = f(x) + f(x) and f(x) = |4x - 1|, then g(-3) = 1 4. Select the statement that is false. A.\tif h(x) = g(x) g(x), then h(x) = (g(x))2 B.\tif 1 f^ xh f^ xh = h^ xh , then g^ xh = h^ xh g^ xh f^ xh C if h(x) = f(x) g(x), then g^ xh = h^ xh ^ h D.\tif f x = h^ xh , then f(x) = h(x) g(x) g^ xh 5. If you are given f^ xh = h(x) = f(x)g(x) is ^ x + 3h and g(x) = 1 - x2, then the domain of A. x $ - 3 x$ 3 B. x$0 C. xdR D. 2 f^ xh while f(x) = x(x + 4) and g(x) = x(x - 2). The g^ xh non-permissible values of h(x) will result in 6. The function h^ xh = A. vertical asymptotes B. points of discontinuity C. a vertical asymptote and a point of discontinuity D. There are no non-permissible values for h(x). Alberta Distance Learning Centre 21 Lesson C - Assignment Booklet Mathematics 30-1: Unit 7 Numeric Response 2 x and g(x) = |4 - 3x|, then (fg)(9) = 2 If f^ xh = 2 + 1 7. Select the statement that is true. 1 A. if h(x) = (fg)(x), then h(x) = f(g(x)) B.\tif h(x) = (fg)(x), then h(x) = g(f(x)) C.\tif h(x) = (fg)(x), then h(x) = (gf)(x) D.\tif h(x) = (fg)(x), then h(x) = f(x)g(x) 8. If you are given h ^ x h = f ^g ^ x hh = 5 1 - 2x and f (x) = 5 x then g(x) = A. 5 ^ xh ^1 - 2xh B. 2 C. 1 - 2x D.\t-2x 9. If you are given f(x) = 2x + 1 + 3 and g(x) = x -1, the range of g(f(x)) is A. y 2 3 1 B. 01y1 3 0 1 y 1 3 C. y 2 1.3 D. 1 10. Which one of the following is not an example of a permutation? 22 A. Three numbers from 0 through 59 are used to open a safe. B. Six numbers from 0 through 49 are selected to enter a lottery. C. Seven digits from 0 through 9 are used to make a phone number. D. Four digits from 0 through 9 are used to make a PIN number. Alberta Distance Learning Centre Mathematics 30-1: Unit 7 1 Lesson C - Assignment Booklet 11. The number of arrangements of the letters of the word success can be found using 7! A. B.\t7! ^3!2!h 7! C. ^3 # 2h 2 D.\t4!3!2! 12. The number of routes from W to Y that pass through X on the grid provided, assuming the path can only move right and down, is W X Y A. 576 B.\t15 C.\t462 D.\t210 Numeric Response 3 2 A family of 5 with a mother, father, and 3 daughters is to be arranged for a photograph. The number of ways this can be done if all four of the females must be standing together is Alberta Distance Learning Centre 23 Lesson C - Assignment Booklet 2 2 13. A hand of 5 cards is dealt from a standard deck of 52 cards. The number of ways that the hand could be made of 2 Kings, 2 Queens, and 1 Ace is A. 4 B.\t144 C.\t576 D.\t792 14. From a group of 4 adults and 3 children, 3 people are to be selected to sing together. If at most 2 adults can be selected, the number of ways the group can be chosen can be calculated using A. 6 C3 3 C1 # 6 C2 B. C. 4 C2 # 3 C1 D. 7 C3 - 4 C3 Numeric Response 4 4 If 12Cr = 924, then r is 2 15. The expansion of (2 - 3x2)10 will include 6 4 A. 10 C4 ^2h ^- 3x2h 8 2 2 B. 10 C2 ^2 h ^- 3x h 24 Mathematics 30-1: Unit 7 C. a negative constant term D.\t15360x2 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 2 2 Lesson C - Assignment Booklet 16. The 4th term in the expansion of (3y - 2x)5, when written in descending powers of y, is A. 720y2x3 B.\t540x2y3 C.\t-720y2x3 D.\t-540x2y3 10 3 3 17. The constant term in the expansion of ` x2 - 4x j is A. 6th B.\t4th C.\t5th D. Does not exist. Numeric Response 5 1 The number of terms in the expansion of (2x - 3y)9 is Alberta Distance Learning Centre 25 Lesson C - Assignment Booklet Mathematics 30-1: Unit 7 Written Response 1. Stu-Gro Inc. earns money cutting grass and cleaning gardens during the summer. The amount they earn from cutting grass can be represented by the function C(n) = 50n - 200 where C(n) is their earnings in dollars and n is the number of lawns cut. Similarly, G(n) = 30n - 75 represents their earnings from cleaning gardens. a. Determine a new function, T(n), that determines their total earnings if all customers have their grass cut and their garden cleaned. 2 b. State the domain and range of T(n). Explain your answers based on the context of the question. 2 c. Determine the number of yards being maintained if the company earns $2525. 1 2. Given f(x) = 2x + 1 and g(x) = 4x2 - 1 2 f a.\tDetermine c m^ xh . g 2 f b. On the grid provided, graph c g m^ xh . y x 26 Alberta Distance Learning Centre Mathematics 30-1: Unit 7 Lesson C - Assignment Booklet f c. Determine the domain and range of c m^ xh . g 3. A store gives its employees a 25% discount on all purchases. During a promotion, all items in the store were reduced by $10. Assume the original price of an item is represented by x. 1 a. Determine the function, E(x), that represents the discounted price the employees pay. 1 b. Determine the function, C(x), that represents the price during the promotion. 1 c.\tDetermine E(C(x)) and C(E(x)). 2 d. Explain why one of these two composite functions gives a better deal to the employee. 2 Alberta Distance Learning Centre 27 Lesson C - Assignment Booklet Mathematics 30-1: Unit 7 4. There are 10 students, 6 females and 4 males who are running for election for the grad committee positions of Chair, Treasurer, and Dance co-ordinator 2 a. Determine the total number of ways the three positions could be filled. 2 b. If it was necessary to have at least one female and at least one male in the three positions, determine the number of ways the three positions could be filled. 5. There are 10 students, 6 females and 4 males, from which a committee of 3 is to be chosen. 2 a. Determine the total number of ways the three positions could be filled. 2 b. If it is decided that the committee cannot be made up of only males or only females, determine the number of ways the committee could be made. 6. A student was asked to examine the expansion of the binomial ` 3 + x2 j . 8 x 1 28 a. Determine the number of terms in the expansion. Alberta Distance Learning Centre Mathematics 30-1: Unit 7 Lesson C - Assignment Booklet 2 b. Determine the middle term in the expansion, first in unsimplified terms and then in simplified terms. 1 c. Will the expansion have a constant term? Explain. Total: 67 Alberta Distance Learning Centre 29 Lesson C - Assignment Booklet Mathematics 30-1: Unit 7 S Standard of Excellence Students need to make connections to other courses to complete. Successful completion shows an ability to think beyond given examples. O Over the acceptable level of understanding Students need to make connections from within the course notes and example to complete. Successful completion shows an ability to draw from given instruction and apply skills to new problems. L Level of acceptable standards Students need to show acceptable levels of understanding to complete. Successful completion shows ability to follow given examples. V Below level of acceptable standards Student's response to question is below acceptable standard. E Inadequate level of acceptable understanding Student's response to question indicates student needs assistance in understanding basic concepts. Thinkstock 30 Alberta Distance Learning Centre