PRINTABLE VERSION Quiz 8 Question 1 1 x + + 3 . (5 ) Find the period for the following function: f (x) = 8 cos a) 2 5 b) 5 c) 10 d) 5 e) 10 f) None of the above. Question 2 Find the phase shift for the following function: f (x) = 3 sin a) units to the left b) 3 units to the right c) 3 units to the left d) 2 units to the left e) units to the right f) None of the above. Question 3 1 x + 2 . (3 ) Give an equation of the form f (x) = A cos(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 3 cos(2 x ) b) f (x) = 3 cos(2 x ) 1 c) f (x) = 6 cos(2 x ) + 1 d) f (x) = 3 cos(2 x ) + 1 e) f (x) = 6 cos(2 x ) 1 f) None of the above. Question 4 Give an equation of the form f (x) = A sin(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 3 sin(4 x 2) b) f (x) = 3 sin(4 x 1 2) c) f (x) = 6 sin(4 x +1 2) d) f (x) = 6 sin(4 x 1 2) e) f (x) = 3 sin(4 x +1 2) f) None of the above. Question 5 List all x -intercepts for y = 3 cos(4x + a) 5 , 12 12 on the interval [ 6 , 2 ]. 3) b) 5 , 12 24 c) , 24 4 d) 0, e) 7 , 24 24 f) None of the above. 7 24 Question 6 Write a sine function with a positive vertical displacement given the following information: the amplitude is 6 , the horizontal shift is 12 to the left, y intercept is (0, 3), and the period is 8 . 1 x + 3 3 (4 ) a) f (x) = 6 sin b) f (x) = 6 sin( x 3 ) 3 4 c) f (x) = 6 sin( x + 3 ) + 3 8 d) f (x) = 6 sin( x + 3 ) + 3 4 e) f (x) = 6 sin f) None of the above. 1 x 3 + 3 (4 ) Question 7 The current I , in amperes, flowing through an AC (alternating current) circuit at time t is I(t) = 200 sin(35 t + a) Period: , where t 0 . Find the period and the horizontal shift. 6) 1 1 , shift to the left. 35 105 b) Period: 1 1 , shift to the right. 35 105 c) Period: 2 1 , shift to the left. 35 420 d) Period: 2 1 , shift to the right. 35 210 e) Period: 2 1 , shift to the left. 35 210 f) None of the above. Question 8 t be the sales function over 1 year where S is sales in thousands of 6 ) dollars and t is time in months, with t = 1 corresponding to January. Which month has maximum Let S(t) = 12.5 4.5 sin( sales? What is the maximum number of sales? a) September; $8, 000 b) March; $8, 000 c) March; $17, 000 d) September; $17, 000 e) June; $17, 000 f) None of the above. Question 9 As a wave passes by, the height of the water is modeled by h(t) = 10 cos 7 t , where h(t) is the ( 9 ) height in feet above mean sea level. Find the height of the wave. (That is, find the vertical distance between the trough and the crest of the wave.) a) 10 b) 10 c) 20 d) 7 9 e) 14 9 f) None of the above. Question 10 7 t approximates the blood pressure P , in millimeters of ( 6 ) The function P(t) = 110 25 sin mercury, at time t , of a person at rest. Find the period and the lowest blood pressure. a) Period: 6 , P min = 135 7 b) Period: 6 , P min = 85 7 c) Period: 12 , P min = 135 7 d) Period: 7 , P min = 60 12 e) Period: 12 , P min = 85 7 f) None of the above. PRINTABLE VERSION Quiz 9 You scored 20 out of 100 Question 1 Your answer is INCORRECT. State the "helper" graph that can be used to assist in graphing the following function: f (x) = 3 csc(x) 2 . a) f (x) = 3 cos(x) 2 b) f (x) = 3 sin(x) 2 c) f (x) = 3 tan(x) 2 d) f (x) = 3 cos(x) 2 2 e) f (x) = 3 sec(x) 2 2 f) None of the above. Question 2 Your answer is INCORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 3 csc( x) 5 ? 3 1 3 2 a) x= b) x = 3 c) x=5 d) x= 3 4 e) x= f) None of the above. Question 3 Your answer is INCORRECT. Find the horizontal shift for the function f (x) = 3 sec( x 1 5 a) to the right 4 b) 5 to the right 4 c) to the left 4 d) 5 to the left 4 e) 10 to the right f) None of the above. 1 ). 4 Question 4 Your answer is INCORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 5 sec(3x a) x= 4 9 b) x= 5 36 c) x= 5 18 d) x= 5 18 1 ? 3 ) 5 72 e) x= f) None of the above. Question 5 Your answer is CORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 5 cot(x) ? a) x= 1 b) x= 1 2 c) x=1 d) x= 1 4 e) x= 1 2 f) None of the above. Question 6 Your answer is INCORRECT. Give an equation of the form f (x) = A tan(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 2 tan(x + 2) + 1 b) f (x) = 2 tan(2 x ) + 1 c) f (x) = 2 tan(2 x ) 1 d) f (x) = 2 tan(2 x) e) f (x) = 2 tan(2 x ) f) None of the above. Question 7 Your answer is INCORRECT. Give an equation of the form f (x) = A csc(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 3 csc(2 x 2) b) f (x) = 6 csc(2 x 1 2) c) f (x) = 3 csc(2 x +1 2) d) f (x) = 6 csc(2 x +1 2) e) f (x) = 3 csc(2 x 1 2) f) None of the above. Question 8 Your answer is INCORRECT. Which of these is a point that lies on the graph of the function y = tan( x) 2? 2 1 a) ( 2 , 1) b) (, 1) c) (, 3) d) 3 ( 2 , 2) e) ( 2 , 0) f) None of the above. Question 9 Your answer is INCORRECT. Determine the period of the function f (x) = 10 cot(5x 9). a) 2 5 b) c) 10 d) 5 e) 5 f) None of the above. Question 10 Your answer is CORRECT. Determine the period of the function f (x) = 5 csc( x 10) . 4 a) 2 b) 4 c) 4 d) 8 e) 2 f) None of the above. PRINTABLE VERSION Quiz 9 You scored 20 out of 100 Question 1 Your answer is INCORRECT. State the "helper" graph that can be used to assist in graphing the following function: f (x) = 3 csc(x) 2 . a) f (x) = 3 cos(x) 2 b) f (x) = 3 sin(x) 2 c) f (x) = 3 tan(x) 2 d) f (x) = 3 cos(x) 2 2 e) f (x) = 3 sec(x) 2 2 f) None of the above. Question 2 Your answer is INCORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 3 csc( x) 5 ? 3 1 3 2 a) x= b) x = 3 c) x=5 d) x= 3 4 e) x= f) None of the above. Question 3 Your answer is INCORRECT. Find the horizontal shift for the function f (x) = 3 sec( x 1 5 a) to the right 4 b) 5 to the right 4 c) to the left 4 d) 5 to the left 4 e) 10 to the right f) None of the above. 1 ). 4 Question 4 Your answer is INCORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 5 sec(3x a) x= 4 9 b) x= 5 36 c) x= 5 18 d) x= 5 18 1 ? 3 ) 5 72 e) x= f) None of the above. Question 5 Your answer is CORRECT. Which of these is an equation of one of the asymptotes of the function f (x) = 5 cot(x) ? a) x= 1 b) x= 1 2 c) x=1 d) x= 1 4 e) x= 1 2 f) None of the above. Question 6 Your answer is INCORRECT. Give an equation of the form f (x) = A tan(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 2 tan(x + 2) + 1 b) f (x) = 2 tan(2 x ) + 1 c) f (x) = 2 tan(2 x ) 1 d) f (x) = 2 tan(2 x) e) f (x) = 2 tan(2 x ) f) None of the above. Question 7 Your answer is INCORRECT. Give an equation of the form f (x) = A csc(Bx C) + D which could be used to represent the given graph. (Note: C or D may be zero.) a) f (x) = 3 csc(2 x 2) b) f (x) = 6 csc(2 x 1 2) c) f (x) = 3 csc(2 x +1 2) d) f (x) = 6 csc(2 x +1 2) e) f (x) = 3 csc(2 x 1 2) f) None of the above. Question 8 Your answer is INCORRECT. Which of these is a point that lies on the graph of the function y = tan( x) 2? 2 1 a) ( 2 , 1) b) (, 1) c) (, 3) d) 3 ( 2 , 2) e) ( 2 , 0) f) None of the above. Question 9 Your answer is INCORRECT. Determine the period of the function f (x) = 10 cot(5x 9). a) 2 5 b) c) 10 d) 5 e) 5 f) None of the above. Question 10 Your answer is CORRECT. Determine the period of the function f (x) = 5 csc( x 10) . 4 a) 2 b) 4 c) 4 d) 8 e) 2 f) None of the above