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\fBack Common Functions Graded Quiz - 30 min . 10 total points Due Sep 4, 11:59 PM WIB 1. h(z) = 51 1 point What type of function is h(I)? O Linear O Quadratic Cubic Exponential 2. What type of function is shown in the graph below? 1 point 10 Root Quadratic Logarithmic O Exponential 3. Which of the following functions has a domain of (-0o, co)? 1 point Select all that apply. O m(z) = Vz +2 O h(1) =23 Of(z) = 212 + 3x - 1 g(z) = O k(z) = 4ez Which of the following functions has no y-intercept? 1 point Select all that apply. Of(z) =ez O v(z) = [[2x] O g(z) = 623 - 4 Oh(z) = 23 O u(I) = VI - 6 5. Compute [[12.9]]. 1 point Enter answer here 6. Find f(8), where f (I) is the following piecewise function. 1 point 3x2 if 1. [ Increases when 0 1. [ Horizontal asymptote at y = 0. Vertical asymptote at z = 0. Has domain (0, oo). Has domain (-00, 00). Has range (0, co). Has range (-0o, 00). O z-intercept at (1, 0). y-intercept at (0, 1). 2. Let b be a positive constant. 1 point elect all of the following statements that apply to the logarithmic function f (z) = log;(I). Decreases when 0 1. Increases when 0 1. Horizontal asymptote at y = 0. OVertical asymptote at z = 0. Has domain (0, co). Has domain (-00, 00). Has range (0, co). OHas range (-00, 00). Oz-intercept at (1, 0). y-intercept at (0, 1). 3. Letg(x) = = +1 eva _ 1' 1 point Find the domain and range of g(I). (Select one answer for each.) Domain: (-00, 00) Domain: (0, 20) Domain: [0, co) O Domain: (1, 00) Domain: [1, 00) [ Range: (-00, 00) O Range: (0, 00) Range: [0, 00) Range: (1, 00) Range: [1, 00) 4- Find all horizontal and vertical asymptotes of g(z) = +1 1 point Select all that apply. O z =1 Dy=1 O y=-1 Dy=0 O z = -1 The function has no horizontal or vertical asymptotes. O z = 0 5. As before, let g(I) = + 1 point Is the function g(z) invertible? If so, find an expression for the inverse function 9 (I). O g 1(z) = 210 O g(z) does not have an inverse. )_ In vi + 1 In VI - 1 (In z)2 + 1 (In z)2 - 1 O gl(z) = 210 7-1 6. Now consider the function h(z) = 1 point In (47) +1 Find the domain and range of h. Domain (-00, 00) Domain (-1, 00) Domain (1 - e, 00) Domain (-1, e - 1) U (e - 1,00) Domain (1 - e, -1) U (-1, 00) O Range (-00, 00) Range (0, 00) Range (1, 00) O Range (-0o, 0) U (0, 00) Range (0, 1) U (1, 00) 7. Find all intercepts of h(3) = z-intercept: (1, 0) O z-intercept: (e - 1, 0) No I-intercept y-intercept: (0, 1) Oy-intercept: (0, -1) No y-intercept 8. Is the function h(z) = In (4 )+ 1" invertible? 1 point If so, find an expression for its inverse. Oh-l(z) = e(1-2)/z - 1 Oh-1(2) = 1-el/v Oh-l(z) = 1/(2+1) +1 1-e(1-2)/2 e(1-2)/2 Oh-1(I) = elly + 1 O h(z) does not have an inverse. ". Evaluate logs (375) ] point Enter answer here 10. Solve for I. 1 point log2(z + 5) + log2(z - 1) = 4 Enter answer here Upgrade to submitBack Modules 1-5 Test - Trigonometric Functions Graded Quiz - 30 min - 10 total points Due Oct 2, 11:59 PM WIB L. A circle of radius 12 is centered at the point O. The circle has a central angle ZAOB which measur es 1450. 1 point 145 B Find the exact measure of ZAOB in radians. Enter your answer as a fraction in lowest terms written in terms of pi. (Do not round to a decimal). Preview will appear here. Enter math expression here 2. As in the previous question, let ZAOB be a central angle of a circle of radius 12, with m.ZAOB = 1450. 1 point What is the length of the intercepted arc AB? Enter your answer as a reduced fraction in terms of pi. (Do not round to a decimal). Preview will appear here. Enter math expression here 3. As in the previous question, let ZAOB be a central angle of a circle of radius 12, with m.LAOB = 1450. 1 point What is the area of the sector defined by LAO B? Enter your answer as a reduced fraction in terms of pi. (Do not round to a decimal). Preview will appear here. Enter math expression here 4. In AABC, m/B = , radians, AC = 34, and tan(LA) = 15. 1 point Find cos(ZA). If your answer is not a whole number, enter it as a fraction in lowest terms. Preview will appear here. Enter math expression here 3. As in the previous question, consider ABC with mLB = 2 radians, AC - 34, and tan(LA) = 15. 1 point Find the area of A ABC. If your answer is not a whole number, enter it as a fraction in lowest terms. Preview will appear here. Enter math expression here 6. Which of the trigonometric functions are bounded? Select all that apply. 1 point O COS I CSC Z O seca O tanz sin a O cota 7. Use trigonometric identities to find the exact value of tan(-75). 1 point Preview will appear here.. Enter math expression here 8. Which of the following is equal to cos(a - B) - cos(a + B)? 1 point O 2 sin a cos B O 2 cos a sin B O 2 sin a sin B O 2 cos a cos B 9. Find a solution I E (-7/2, 7 /2) for the following equation: a point (sec z + csc z) (sin z + cos I) = cot z + 1 Preview will appear here. Enter math expression here 10. Let f (I) = sin(2:) + 1 1 point Select an answer for each of the following: (a) Find the domain of f (I). (b) Find the range of f (I). (c) Find the period of f (). (d) Is f (z) even or odd? Domain: All real numbers I Domain: All real numbers I # 7 + 2kx for integers k Domain: All real numbers z * S + + ki for integers k Domain: All real numbers z # 7 + 2kx for integers k [ Range: (-00, 00) Range: (1/2, 00) Range: [1/2, 00) Range: (-00, 1/2) U (1/2, 00) O Period: 27 Period: T O Period: 7 /2 Of(z) is not periodic Of(z) is an even function O f(z) is an odd function Of(z) is neither even nor odd Upgrade to submitBack Modules 1 and 2 Test - Functions Graded Quiz - 30 min - 10 total points Due Sep 11, 11:59 PM WIB 1. The piecewise function f (I) is graphed below. Find the range of f. 1 point O (-4, 4] O (-4, 0) U (0, 4] O [-2,4) O (-4,-2) U(-2, 0) U (0, 4] O (-2, 4) O (-2, 1) U (1, 4) 2. Leth(z) _ 3(2 + 2)(27 -22 + 1) . What is the domain of h(3)? 1 point (12 -1) None of these O (-00, -1) U (1, 00) O (-00, 00) O (-00, -1) U(-1,00) O (-00, -1) U(-1,1) U (1, 00) 3. Let a, b, c, d be fixed numbers, and suppose that a * 0 and a * 1. 1 point Which of the following types of common functions are one-to-one for any chosen values of a, b, c, and d? Select all that apply. O The linear function y = az + b The quadratic function az? + ba + c The cubic function y = ar + ba? + ca + d The exponential function y = a# (suppose a > 0) The logarithmic function y = loga(I) (suppose a > 0) The line L1 passes through the points (-3, -2) and (6, 4). The line Ly passes through the point (5, -1) and is perpendicular to L1. 1 point Find the coordinates of the point where L1 and L2 intersect. Enter your answer in the form (x,y). If your answer is not a whole number, then input it as a decimal. Enter answer here 5. You are planning to rent a car for one day, and Syzygy Car Rental Company offers two different plans. 1 point With the Limited Miles plan, and 25 cents for each mile driven. With the Unlimited Miles plan, you are charged a flat rate of $62 per day. What is the maximum number of miles you can drive in one day so that the Limited Miles plan costs less than or the same as the Unlimited Miles plan? Round your answer to the nearest mile (whole number). Enter a number only, no units. Enter answer here 6. While flying at an altitude of 81 feet, a seagull drops a French fry. The height (in feet) of the French fry at time t (in seconds) is modeled by the function h(t) = 1 point -16t2 + 81. After how many seconds does the French fry hit the ground? if necessary, round your answer to the nearest hundredth of a second. Enter a number only, no units. Enter answer here 7. An arrow is shot into the air. Its height is given by the function y(r) = 64x + 46 - 1612, where y is measured in yards and I is measured in seconds. 1 point What is the maximum height (in yards) that the arrow reaches? If necessary, round your answer to the nearest hundredth of a yard. Enter a number only, no units. Enter answer here 8. The Throckmorton Company models its monthly revenue (in dollars) from the sale of I items with the function R(x) - 35x - 0.2512. The company has a fixed cost 1 point of $540 per month and a variable cost of $3 per item. H e company sell to break even? If necessary, round up to the nearest item (whole number). Enter a number only, no units. Enter answer here 9. Let f(z) = 3x2 + 2,g(x) = VI + 1, and h(x) = . Find an expression for (f ogoh)(z) for z > 0. 1 point (fogoh)(z) = 3+ 5x O (fogoh)(1) = V312 +3 22 + 5 O (fogoh)(1) = (fogoh)(z) - V32 + 3 10. Let f (z) = 121 -1 2x + 4 . Find an expression for f-1(I). 1 point Of-1(z) = 23 + 4 12x - 1 -4x - 1 Of l(1) = 21 - 12 Of-1(z) 12x - 1 21 + 4 4x + 1 Ofl(z) = 2x - 12 Upgrade to submitBack Properties of Logarithmic Functions Due Sep 25, 11:59 PM WIB Graded Quiz . 30 min . 10 total points 1. Use the logarithm rules to write the expression as a single logarithm. 1 point 2 In(z) - In(y + 1) + 3In(z) 6:z O In (y+1 O In(12 + 23 - y -1) O In(2z + 3z - y - 1) In y+1 7223 2. Use the logarithm rules to simplify the expression. 1 point eln(1)+2 In(y) O ezzy O 2ry O ery 3. Evaluate the logarithm. If necessary, write your answer as a decimal rounded to the nearest tenth. 1 point logs 1257 V3125 Enter answer here 4. Evaluate the logarithm. If necessary, write your answer as a decimal rounded to the nearest tenth. 1 point 3 1 2 Enter answer here 5. Solve for T. If necessary, enter your answer as a decimal rounded to the nearest tenth. 1 point logA(I) + log4(z + 12) = 3 Enter answer here Solve for T. If necessary, enter your answer as a decimal rounded to the nearest tenth. 1 point log2(2x) - 2 log2(I - 1) = 2 Enter answer here 7. Solve for T. If necessary, enter your answer as a decimal rounded to the nearest tenth. 1 point In (Vz) - 2 In(2) = 0 Enter answer here Solve for T. If necessary, enter your answer as a decimal rounded to the nearest tenth. 1 point 2 In(x) - In(2:) = 0 Enter answer here 9. Solve for I. 1 point (In x)2 - 9=0 Oz = -3orz = 3 Or = e3 No solutions O 1 = 3 Oz = gort = e3 10. Solve for T. point log:(3 - z) + logg(2x + 18) = 2 O = = -1 O T = 1 orz = 5 No solutions O T= -1orz = -5 Of =5 Upgrade to submitBack Right Triangle Trigonometry Graded Quiz - 30 min . 10 total points Due Sep 11, 11:59 PM WIB 1. AABC is a right triangle with hypotenuse AC. If AB = 24 and BC = 10, what is tan ZA? 1 point O O O O 2. ADEF is a right triangle with hypotenuse DF. If DE = 8 and EF = 15, what is cos ZD? 1 point O O C / 001 07 - 1 0c 17 O 3. If sin 0 = = 29 and cos 0 = 29, then what is tan 0? 1 point Cannot be determined O 29 20 20 O 4. If sin 0 = o and tan 0 = 13 then what is cos 0? 1 point D O O Cannot be determined 85 13 13 5. ADEF is a right triangle, where ZE = 90%, EF = 24, and tan LF = 12 . Find the area of ADEF. 1 point For your answer, enter a number only (no units). Enter answer here If 0 is an acute angle and sin(0) = 2, then what is the measure of 0 in degrees? 1 point For your answer, enter a number only (no units). Enter answer here 7. If cos 0 > 0 and sin 0 5ft . min Valid O Invalid 7. Based on the rules of dimensional analysis, determine whether the following computation is valid or invalid. 1 point 7K . 5g - 2kg O Valid Invalid The ideal gas law relates the volume, pressure, and temperature of a gas with the equation 1 point PV = nRT where P is the pressure, V is the volume, n is the amount of substance, and T' is the temperature. R is a constant called the ideal gas constant. Determine the dimension [R]. O [R] = MLAT 'NO O [R] = ML'T-2Ne O [R] = ML'T-2N-10-1 O [R] = ML-'T-'N-10-1 9. Supposey = debt + c, where the number e is dimensionless, [a] = NL , and [t] = T. 1 point Determine the dimension [6]. O [b] = T O [b] = T-1 O [6 ] = N-L [6] = NL-1 O b is dimensionless 10. When a ball is tossed, its trajectory fits the shape of a parabola. The ball's height h is modeled by the function h(t) = at + bt + c, where t is measured in seconds. 1 point Find the dimensions of the constants a, b, c. O [a] = L, [b] = LT , [c] = LT- O [a] = [6] = [c] = L O [a] = TL-2, [6] = TL-1, = T O [a] = LT 2, [b] = LT-1, = L O [a] = T, [b] = TL-1, [c] = TL-z O a, b, care dimensionless Upgrade to submitBack Due Sep 18, 11:59 PM WB If there is linear correlation between z and In y, which O Exponential function O Power function O Linear function O Logarithmic function 2. Which of the folkart OMonthly revenue for a ce ONone of these O Size of a bacteria populatio O Monthly sales at an ice cream shop, recorded over a period of 10 years O Number of cigarettes smoked daily and blood pressure, recorded for all patients at a clinic 3. Which of the following function types always has a y-intercept? O Exponential function O Power function O Both exponential and power functions O Neither exponential nor power functions expectancy (in years) for a selection Life Expect Which type of function -60 -40 20 2 -1 0 1 2 3 4 5 6 7 8 9 10 O Power O Logarithm Which type of function would best fit the data in this scatterplot? . . . . . 10 10 20 30 40 50 O Logari O Trigonometric Linear Expone 7. Which type of 60 40 20 2 -1 0 O Linear O Trigonometric O Power A = 6.54In(D) - 8.61 e in years and D is the dia meter of 3 feet. A = -18sin (6) +59 where A is the temperature measured "presents January 2000). Use the model to predict the average temperature in Atlantic City in August 2001. Enter a number only (no units). Round your answer to two decimal places. mer answer here model the number of species of bats, S, as a power function of the island's area, A. When they create a log log plot of In A and In S, the least squares ro fon line has the equation y = 0.08Ba + 4.175. d the power function model A($). O S - Is AL ITS O S = 0.0884 4175 O s - (RAA+4.175 Upgrade to suberitDue Step 4, 13:50 PM WIG 1. A real estate firm is trying to determine what factors lead a home to sell for a higher price. They collect the folio Price (dollars) Living Area (square feet) 142212 1982 134865 1676 118007 1694 138297 1800 129470 206512 50709 108794 68353 123266 309808 157946 80248 135708 140510 151917 235105 2577 211517 2328 What is the response variable? Price O Number of Rooms O Living Area 2 . What does the mination R represent? The proportion of the variation in the response variable that can be explained by the explanatory variable The strength of linear relationship between the explanatory and response variables sponse variable that is directly caused by the explanatory variable O The strength of quadratic relationship between the explanatory and response variables 3. True or false? If 7 = 1, then changes in the response variable are caused by changes in the explanatory variable. True False 4. Which of the fo lation coefficient r for the data plotted below? Or = 0.818 Or = -0.771 OT =-0.4 Or = 0.081 3. Which of the following could be the value of the correlation coefficient T for the data plotted below? 109000 209060 309090 209090 500000 600090 O -0.75 O -0.082 0.082 0.759 6. Which of the followin we of r for a data set? Changing the units used to meas None of these. O Removing points from the data set. Adding points to the data set. Height of jump (meters) 1980 the height of the winning jun right of the B Strong O Weak positive co Weak negative O Strong negative correlation O No correlation of doctors per person to the average life expectancy in that country. Their findings are displayed in the scatterplot below, . . . . 8 801 0.02 doctors per por sudd Y = 309.25x + 36.85 The equation of the least squares regression line is y = 369.25x + 54.85, where y represents life expectancy and a represents doctors per person. Use the linear model to predict the life expectancy in a country that has 36 doctors for every 1000 people (that is, 0.036 doctors per person). Round your answer to the nearest year. Use the linear model from the previc 75 years. Round your answer to the nearest doctor. Enter answer here The line with minimal vertical squared distances from the data points. The line which passes through the maximum number of data points. dation coefficient T. ontal squared ofstances from the data points. The line whose slope matches the coefficient of determination R2. Upgrade to submitBack Sine and Cosine Functions Due Sep 18, 11:59 PM WIB Graded Quiz - 30 min - 10 total points 1. Use a calculator to evalute cos - rad ). Round your answer to four decimal places. 1 point Enter answer here 2. Which of the following expressions is equal to cos(27 - 0)? 1 point O - sin(0) O cos(0) O sin(0) O - cos(0) 3. Let k(x) = 2 cos (x). What is the range of k(I)? 1 point O (-1, 1) O (-1,1) O [-1, 1] O [-2, 2] O [-1,1] O (-2, 2) 4. Letk(x) = 2 cos (ZI). What is the period of k(I)? 1 point Preview will appear here... Enter math expression here Find sin(0) if 8 is in Quadrant IV and cos(0) 25 1 point Enter your answer as a fraction in lowest terms. Preview will appear here... Enter math expression here Which of the following is equivalent to the expression? 1 point cost + sin a tan c O 1 cos Z O 1 tan a 0 1 sin r sin' z O cos' I 7. Find all t E [0, 27] such that 2 sin t + 7 cost = 5. 1 point Ot= O No solution Ot= 117 6 0 6 Ot = Ot= or - 8. Leth(x) = sin (2 . Is h(z) odd or even? 1 point O Odd Even ONeither odd nor even Let f (I) sin' (I) . What is the domain of f (I)? 1 point cos(I) All real numbers I except = , + 2km for integers k All real numbers I except = , + ki for integers k All real numbers I except a = KT for integers k All real numbers I All real numbers I except I = 2km for integers k 10. Let h(z) = sin ( . Find two functions f (z) and g(z) such that h(z) = (fog)(I). 1 point Of(z) = sin (z),g(1) = 12 Of(I) = sin z ' 9 (2) = Of(I) = sin(z),g(z) = 72 O f(z) = 12,9(1) = sin I Of(z) = 29(z) = sin(z) Upgrade to submitBack The Tangent and Other Periodic Functions Due Sep 25, 11:59 PM WIB Graded Quiz . 30 min . 10 total points 1. Evaluate cot () 1 point Do not write your answer as a decimal. Use exact values instead For square roots, write sqrt(). For example, to write v 2 you would input sqrt(2). Preview will appear here... Enter math expression here 2. Use a calculator to evalute cot (84). 1 point Round your answer to four decimal places. Enter answer here If 0 is an angle in Quadrant II and sin(0) = 12 13) then what is sec(0)? 1 point Enter your answer as a fraction in lowest terms. Preview will appear here... Enter math expression here What is the domain of cSC T? 1 point All real numbers T except = = kn, k = 0, +1, 12,... All real numbers T except x = 2kn, k = 0, +1, 12, ... All real numbers I except = = , + kx, k = 0, 41, 12, ... All real numbers I All real numbers a except : = , + 2km, k = 0, 41, 42, ... 5. Which of the following are odd functions? Select all that apply. 1 point tani sec O cot CSC I None of these are odd functions 6. Find the range of 2 tan(2x). 1 point O (-00, -4] U [4, 00) O (-00, -2] U [2, 00) O (-00, -2) U (2, 00) O (-00, -4) U (4, 00) O (-00, 00) 7. Find the period of f () = tan(2x). 1 point Preview will appear here... Enter math expression here 8. Find a solution : in the interval [0, 27). point sin'(z) + tan?(x) = sec?(z) - 2 - OF O 1= 7 Or A No solutions 9. Viewed from a point on the ground 100 feet from its base, the angle of elevation to the top of a steeple is 750. How high is the steeple? 1 point Round your answer to the three decimal places. Enter answer here 10. If sec 0 0, then in which quadrant does O lie? point O Quadrant | Quadrant II O Quadrant III O Quadrant IV Upgrade to submit