ࡱ> %Ioa{ ~ c  ٚbjbj ee:JJv" eA$-LRLRLRtR@@@@@@@$CFT@@JJLRtRqB A^JLR(tR@@^5?tR- 9h@)A<eA9FF?F?4t4@@ReAF : Applications Round all final answers correctly to one decimal unless the question says otherwise. At the Luanda port, the depth of the water h metres at time t hours during a certain day is given by the formula  EMBED Equation.3 . Determine the amplitude, period, phase shift and vertical shift. Use the information to sketch the function over a 24 hour interval. Determine the maximum water depth and the time(s) it occurs. Determine the depth of the water at 6:30 a.m. and 7:30 p.m. At Yourtown, the time of the sunrise on the nth day of the year is given by the formula.  EMBED Equation.3 . Determine the time, to the nearest minute, that the sun rises on October 20 (day 293). What is the earliest sunrise and on what day does it occur? Round the time to the nearest minute. Given the function  EMBED Equation.3 , where h is the height of an object in metres relative to the ground at any time t seconds. Determine the period of the function. Determine the minimum value and when it occurs. Determine the height after 15 seconds. Determine all values of t such that the object is 6 m above the ground. A Ferris wheel with a radius of 20 m rotates once every 40 s. Passengers get on at the lowest point which is 1 m above the ground. Draw a graph showing your height above the ground during the first two cycles. Write an equation which expresses your height as a function of time on the ride. Calculate your height above the ground after 15 s. At what times will the rider be 30 m above the ground? At what times in the first rotation will the rider be 25 m or higher above the ground? NOTE: An algebraic solution is required but refer to your graph from part a) to interpret your answers. 5. Tidal forces are the greatest when the Earth, the sun, and the moon are in line. When this occurs at the Annapolis Tidal Generating Station in Nova Scotia, the water has a maximum depth of 9.6 m at 4:30 a.m. and a minimum depth of 0.4 m approximately 6 hours later. a) Write an equation for the depth of the water at any time t. b) Calculate the depth of the water at 9:30 a.m. and 6:45 p.m. c) At what times during the day will the water be at least 9 m deep? Round your times to the nearest minute. A sketch may be helpful in interpreting your answers. 6. The pedals of a bicycle are mounted on a bracket whose centre is 30 cm above the ground. Each pedal is 16 cm from the bracket. The bicycle is pedalled at 6 cycles per minute. Assume that you start pedalling with the pedal at the highest position at t = 0. a) Draw a graph showing the height of the pedal above the ground during the first minute. b) Determine the amplitude, period, and vertical shift. c) Write an equation to represent the height of the pedal as a function of time. d) Determine the height of the pedal after 25 seconds. e) At what times in the first 30 seconds will the pedal be 15 cm above the ground? Round your times to the nearest tenth of a second. f) At what times will the pedal be at least 15 cm above the ground? Answers 1. a) amp = 1.5, period = 12, ps = 4, vs = 3.1 c) max depth = 4.6 m,  EMBED Equation.3  1. d) 4.5 m, 4.5 m 2. a) 5:28 a.m. b) 4:31 a.m. on day 354 (December 20) 3. a) period = 12.4 b) min = 1.8 m when  EMBED Equation.3  c) 6.4 m 3. d) 3.1 s and 12.3 s; in general,  EMBED Equation.3  4. b) if ps = 0,  EMBED Equation.3  OR  EMBED Equation.3  c) 35.1 m 4. d) 13.0 s and 27.0 s; in general,  EMBED Equation.3  4. e) between 11.3 s and 28.7 s 5. a) if ps = 4.5,  EMBED Equation.3 ; if ps = 1.5,  EMBED Equation.3  5. b) 1.0 m, 6.8 m 5. c) between 3:31 a.m. and 5:29 a.m. and between 3:31 p.m. and 5:29 p.m. 6. b) amp = 16, period = 10, vs = 30 c) if ps = 0,  EMBED Equation.3  d) 14 cm 6. e) 4.4 s, 5.6 s, 14.4 s, 15.6 s, 24.4 s, 25.6 s 6. f) between: 0 s and 4.4 s & 5.6 s and 14.4 s & 15.6 s and 24.4 s & 25.6 s and 30 s UNIT #6 Review 1. Convert each degree to radian measure in terms of (. a) 45b) 300c) -210 2. Convert each radian measure to degrees. If the answer is not exact, round correctly to one decimal place. a)  EMBED Equation.3 radb)  EMBED Equation.3  rad c) 6 rad d) 3.5( rad 3. Find the length of the arc of a circle with radius 40 cm and central angle 50. State the exact answer and the answer accurate to 3 decimal places. (The central angle is the angle subtended at the centre of the circle by the arc.) 4. In a circle, the arc length is 9 mm and the angle subtended at the centre is  EMBED Equation.3 . What is the exact area of the circle? Determine the related acute angle associated with each of the following standard position angles. Provide a clearly labelled sketch. a)  EMBED Equation.3 b)  EMBED Equation.3 c)  EMBED Equation.3 d) 4.25 6. ( is in standard position with its terminal arm in the quadrant 4, sin( =  EMBED Equation.3 , and 0 < ( < 2(. Provide a clearly labelled sketch. Determine the exact value of cos( and tan(. 7. For each of the following, (i) sketch the standard position angle (ii) determine the related acute angle (iii) determine the exact value of the specified trigonometric ratio. Do not use a calculator. a) tan  EMBED Equation.3 b) sin  EMBED Equation.3 c) cos EMBED Equation.3 d) tan  EMBED Equation.3  8. Solve each of the following equations to two decimal places,  EMBED Equation.3 . a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  9. Solve each of the following equations. Give exact answers only,  EMBED Equation.3 . a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  10. Solve each of the following equations. a)  EMBED Equation.3 ,  EMBED Equation.3 , correct to two decimal places b)  EMBED Equation.3 ,  EMBED Equation.3 , exact answers. 11. Solve  EMBED Equation.3 for x,  EMBED Equation.3 . Give exact answers. Hint factor. 12. On the same grid, sketch each of the following pairs of graphs. Clearly label all asymptotes and zeroes. Review the features of the various trigonometric functions.  a)  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3  b)  EMBED Equation.3  EMBED Equation.3  c)  EMBED Equation.3  For each of the following functions, i) determine the amplitude, period, phase shift and vertical shift; ii) graph at least one complete period; and iii) state the domain and range. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation  d)  EMBED Equation  14. Determine the equation of a cosine function with maximum value 5, minimum value -9, period  EMBED Equation.3  and phase shift  EMBED Equation.3 . 15. Determine the equation of a sine function with a minimum at ( EMBED Equation.3 ,0) and a maximum at  EMBED Equation.3 . For each of the following trigonometric equations: ( Write the amplitude, period, phase shift & vertical shift. ( Write the equation of the function. 16. Cosine Function Equation: ________________________________  Amplitude = _____ Period = _____ Phase Shift = _____ Vertical Shift. = _____ 17. Sine Function Equation: ___________________________________  Amplitude = _____ Period = _____ Phase Shift = _____ Vertical Shift. = _____ Given the function, EMBED Equation.3 : Determine the domain and range. Determine the amplitude, period, phase shift and vertical shift. Determine d, accurate to one decimal place when t = 11. Determine all values of t such that d is 8. State the exact answers. A Ferris wheel with a diameter of 36 m rotates three times every two minutes. Passengers get on at the lowest point which is 6 m above the ground. Draw a graph showing the height of the rider above the ground during the first two minutes. Write an equation which expresses your height as a function of time on the ride. Calculate the exact height above the ground after 25 s. At what times in the first two rotations will the rider be 10 m or less above the ground? Answers 1. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  2. a) 150( b) 405( c) 343.8( d) 630( 3.  EMBED Equation.3 cm, 34.907 cm 4.  EMBED Equation.3 mm2 5. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  d) 1.11 6.  EMBED Equation.3  7. a) 1 b)  EMBED Equation.3  c)  EMBED Equation.3  d) undefined 8. a) 3.28, 6.15 8. b) 1.32, 4.96 c) 2.82, 5.96 9. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  10. a) 1.25, 2.94 10. b)  EMBED Equation.3  11.  EMBED Equation.3  12. refer to course notes 13. a) i) a=2, period= EMBED Equation.3 , ps= EMBED Equation.3 , vs=0 13. a) iii) D= EMBED Equation.3 , R= EMBED Equation.3  b) i) a=1, period= EMBED Equation.3 , ps= EMBED Equation.3 , vs=0 iii) D= EMBED Equation.3 , R=  EMBED Equation.3  13. c) i) a=3, period= EMBED Equation.3 , ps= EMBED Equation.3 , vs=-2 iii) D= EMBED Equation.3 , R= EMBED Equation.3  d) i)a=0.5, period= EMBED Equation.3 , ps= EMBED Equation.3 , vs = 2.5 13. d) iii) D= EMBED Equation.3 , R= EMBED Equation.3  14.  EMBED Equation.3  15.  EMBED Equation.3  OR  EMBED Equation.3  16. a=1.5, period= EMBED Equation.3 , ps= EMBED Equation.3 , vs=1,  EMBED Equation.3  17. a=2, period= EMBED Equation.3 , ps=0, vs=2,  EMBED Equation.3  18. a) D= EMBED Equation.3 , R= EMBED Equation.3  b) a=4, period=20, ps=3, vs=6 c) 8.4 d)  EMBED Equation.3  19. b) a=18, period=40, vs=24, if ps=0 then  EMBED Equation.3  c)  EMBED Equation.3  19. d) between: 0 and 4.3 seconds, 35.7 and 44.3 seconds, and 75.7 and 80 seconds Trigonometric Identities  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Trigonometric Identities 1. Prove the following trigonometric identities. a)  EMBED Equation.3 b)  EMBED Equation.3 c)  EMBED Equation.3 d)  EMBED Equation.3 e)  EMBED Equation.3 f)  EMBED Equation.3 g)  EMBED Equation.3 h)  EMBED Equation.3 i)  EMBED Equation.3  2. Prove: (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d)  EMBED Equation.3  3. Prove: (a)  EMBED Equation.3  (b)  EMBED Equation.3  4. Prove: (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  5. Prove: (a)  EMBED Equation.3  (b)  EMBED Equation.3  6. Prove: (a)  EMBED Equation.3  (b) EMBED Equation.3  Cofunction Identities Write each of the following in terms of the cofunction identity. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3  f)  EMBED Equation.3  Write  EMBED Equation.3  in terms of secant. Recall that cosecant is the reciprocal of the sine function and secant is the reciprocal of the cosine function. Answers: 1. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3  f)  EMBED Equation.3  2.  EMBED Equation.3  More Trigonometric Identities Prove the following trigonometric identities. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3  Prove the following trigonometric identities. a)  EMBED Equation.3  b)  EMBED Equation.3  CHALLENGE: Prove:  EMBED Equation.3 . You may use your results from page 503 #8. Equations and Identities Solve the following equations for x,  EMBED Equation.DSMT4 . State exact answers where possible; otherwise, state answers accurate to two decimal places. 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6.  EMBED Equation.DSMT4  7.  EMBED Equation.DSMT4  8.  EMBED Equation.DSMT4  Answers: 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6.  EMBED Equation.DSMT4  7.  EMBED Equation.DSMT4  8.  EMBED Equation.DSMT4  Prove the following trigonometric identities. 9.  EMBED Equation.DSMT4  10.  EMBED Equation.DSMT4  11.  EMBED Equation.DSMT4  12.  EMBED Equation.DSMT4  13.  EMBED Equation.DSMT4  14.  EMBED Equation.DSMT4  15.  EMBED Equation.DSMT4  16.  EMBED Equation.DSMT4  17.  EMBED Equation.DSMT4  Trigonometric Equations Involving Different Functions Solve the following equations for x,  EMBED Equation.DSMT4  State the exact answers where possible. Otherwise round correctly to three decimal places. 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6.  EMBED Equation.DSMT4  7.  EMBED Equation.DSMT4  8.  EMBED Equation.DSMT4  9. Find the exact points of intersection of  EMBED Equation.DSMT4  on the domain  EMBED Equation.DSMT4  10. We know that  EMBED Equation.DSMT4  is an identity and hence is true for all values of x. However,  EMBED Equation.DSMT4 is not an identity. Over the interval  EMBED Equation.DSMT4 , determine the values of x for which the equation is satisfied. You may have to check your answers when done. [HINT: squaring both sides carefully may help.] Answers 1.  EMBED Equation.DSMT4  2.  EMBED Equation.3  3.  EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6. 2.944, 6.086 7.  EMBED Equation.DSMT4  8.  EMBED Equation.DSMT4  9.  EMBED Equation.DSMT4  10.  EMBED Equation.DSMT4  Key Features of Functions Sketch the following polynomial functions and identify the key features: the x-intercept(s), y-intercept, degree of the polynomial function , number of zeroes, end behaviours and finite differences. a)  EMBED Equation.3  b)  EMBED Equation.3  Sketch the following exponential and logarithmic functions and identify the key features: domain, range, equation of the asymptote, end behaviours, increasing/decreasing function, x-intercept(s), y-intercept and finite differences. a)  EMBED Equation.3  b)  EMBED Equation.3  Sketch  EMBED Equation.3  and identify the key features: vertical and horizontal asymptotes, domain, range, x-intercept(s), y-intercept, increasing intervals, decreasing intervals, positive intervals and negative intervals. Sketch  EMBED Equation.3  and identify the key features: vertical and horizontal asymptotes, domain, range, x-intercept(s), y-intercept, increasing intervals, decreasing intervals, positive intervals and negative intervals. Sketch  EMBED Equation.3  and identify the key features: vertical, horizontal and linear oblique asymptotes, x-intercept(s) and y-intercept.  Answers 1. a) x-ints -3,1,4; y-int -12; degree 3; 3 zeroes  EMBED Equation.3  The difference table shows third differences of y have a constant value of -6 for constant (x. b) x-ints -1,2,  EMBED Equation.3 ,  EMBED Equation.3 ; y-int 8; degree 4; 4 zeroes  EMBED Equation.3  The difference table shows fourth differences of y have a constant value of 24 for constant (x.  2. a) vertical asymptote x=-1; no y-int; x-int -1.6  EMBED Equation.3 ;  EMBED Equation.3  increasing: none; decreasing:  EMBED Equation.DSMT4   EMBED Equation.3  The difference table shows a constant ratio of 2  between first differences of x values for constant (y.  b) horizontal asymptote y=-5; y-int  EMBED Equation.DSMT4 ; x-int 4.7  EMBED Equation.3 ;  EMBED Equation.3  increasing:  EMBED Equation.DSMT4 ; decreasing: none  EMBED Equation.3  The difference table shows a constant ratio of 2 between first differences of y values for  constant (x. 3. vertical asymptote x=3; horizontal asymptote y=0 y-int  EMBED Equation.DSMT4 ; no x-int;  EMBED Equation.3 ;  EMBED Equation.3   4. vertical asymptote x=2; horizontal asymptote  EMBED Equation.DSMT4  y-int  EMBED Equation.DSMT4 ; x-int 3;  EMBED Equation.3 ;  EMBED Equation.3  positive:  EMBED Equation.3 ; negative:  EMBED Equation.3 ; increasing: none; decreasing:  EMBED Equation.3    5. vertical asymptote x=3; no horizontal asymptote; linear oblique asymptote y=x+9; y-int  EMBED Equation.DSMT4 ; x-int -4,-2 More Working with Intercepts 1. For each of the following: State the domain State the range. Determine the xintercepts. State exact answers, then accurate to two decimal places. Determine the exact value of the yintercept.  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  2. For each of the following: a) Determine the amplitude, vertical shift, period and phase shift. b) Determine the maximum, minimum, domain and range. c) Determine the exact value of the yintercept, if possible; otherwise, state answers accurate to two decimal places. d) Determine the exact value of the x-intercept(s) in one period, if possible; otherwise, state answers accurate to two decimal places. Determine the exact value of all zeroes, if possible; otherwise, state answers accurate to two decimal places. i)  EMBED Equation.3  ii)  EMBED Equation.3  iii)  EMBED Equation.3  iv)  EMBED Equation.3  Answers:  1. i) Domain =  EMBED Equation.3 , Range =  EMBED Equation.DSMT4 , x-int =  EMBED Equation.3  (= 2.20), y-int =  EMBED Equation.3  ii) Domain =  EMBED Equation.3 , Range =  EMBED Equation.DSMT4 , x-int =  EMBED Equation.3  (= -0.18), y-int = -2 iii) Domain =  EMBED Equation.DSMT4 , Range =  EMBED Equation.3 , x-int =  EMBED Equation.3 , y-int =  EMBED Equation.3  2. i) a) amp = 5, vs = 4, period =  EMBED Equation.3 , ps = 0 b) maximum = 9, minimum = -1 Domain =  EMBED Equation.3 , Range =  EMBED Equation.3  c) y intercept = 4 d) x intercepts =  EMBED Equation.3  e) zeroes  EMBED Equation.3  2. ii) a) amp = 2, vs = 1, period =  EMBED Equation.3 , ps =  EMBED Equation.3  b) maximum = 3, minimum = -1 Domain =  EMBED Equation.3 , Range =  EMBED Equation.3  c) y intercept =  EMBED Equation.3  d) x intercepts =  EMBED Equation.3  e) zeroes  EMBED Equation.3  2. iii) a) amp = 4, vs = 6, period =  EMBED Equation.DSMT4 , ps =  EMBED Equation.3  b) maximum = 10, minimum = 2 Domain =  EMBED Equation.3 , Range =  EMBED Equation.3  c) y intercept = 4 d) x intercepts = none e) zeroes: none 2. iv) a) amp = 3, vs = -3, period =  EMBED Equation.3 , ps =  EMBED Equation.3  b) maximum = 0, minimum = -6 Domain =  EMBED Equation.3 , Range =  EMBED Equation.3  c) y intercept = -4.03 d) x intercept =  EMBED Equation.3  e) zeroes  EMBED Equation.3  Sum and Differences of Functions 1. Given the functions  EMBED Equation.3  and  EMBED Equation.3 , i) i) State the domain of  EMBED Equation.3 . ii) State the domain of  EMBED Equation.3 . iii) Find  EMBED Equation.3  and state the domain. iv) Find  EMBED Equation.3  and state the domain. v) Find  EMBED Equation.3  and state the domain.  a)  EMBED Equation.3  and  EMBED Equation.3  b)  EMBED Equation.3  and  EMBED Equation.3  c)  EMBED Equation.3  and  EMBED Equation.3  d)  EMBED Equation.3  and  EMBED Equation.3  2. Given the functions  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3 . e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3 . 3. Given the functions  EMBED Equation.3  and  EMBED Equation.3 , a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3 . e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3 . g) Determine  EMBED Equation.3  and state the domain. h) Find the exact value of  EMBED Equation.3 . Then, find accurate to two decimal places. 4. Given the functions  EMBED Equation.3  and  EMBED Equation.3 , a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find the exact value of  EMBED Equation.3 . e) Determine  EMBED Equation.3  and state the domain. f) Find the exact value of  EMBED Equation.3 . g) Determine  EMBED Equation.3  and state the domain. h) Find the exact value of  EMBED Equation.3 . ANSWERS: 1. a)  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3  b)  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3 ;  EMBED Equation.3  2. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  3. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3   e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h)  EMBED Equation.3  4. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h)  EMBED Equation.3  Products and Quotients of Functions 1. Given the functions  EMBED Equation.3  and  EMBED Equation.3 , i) i) State the domain of  EMBED Equation.3 . ii) State the domain of  EMBED Equation.3 . iii) Find  EMBED Equation.3  and state the domain. iv) Find  EMBED Equation.3  and state the domain. v) Find  EMBED Equation.3  and state the domain.  a)  EMBED Equation.3  and  EMBED Equation.3  b)  EMBED Equation.3  and  EMBED Equation.3  c)  EMBED Equation.3  and  EMBED Equation.3  2. Given the functions  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3 . e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3 . g) Determine  EMBED Equation.3  and state the domain. h) Find  EMBED Equation.3 . 3. Given the functions  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find the exact value of  EMBED Equation.3 . Then, state accurate to two decimal places. e) Determine  EMBED Equation.3  and state the domain. f) Find the exact value of  EMBED Equation.3 . Then, state accurate to two decimal places. g) Determine  EMBED Equation.3  and state the domain. h) Find the exact value of  EMBED Equation.3 . Then, state accurate to two decimal places. 4. Given the functions  EMBED Equation.3  and  EMBED Equation.3 , a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find the exact value of  EMBED Equation.3 . e) Determine  EMBED Equation.3  and state the domain. f) Find the exact value of  EMBED Equation.3 . g) Determine  EMBED Equation.3  and state the domain. h) Find the exact value of  EMBED Equation.3 .  ANSWERS: 1. a)  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3  (hole at x = -2);  EMBED Equation.3   EMBED Equation.3  (hole at x = -2);  EMBED Equation.3  b)  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3  (hole at x = -1 is outside  EMBED Equation.3 ) ;  EMBED Equation.3   EMBED Equation.3  (hole at x = -1 is outside  EMBED Equation.3 );  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3  (hole at x = -6);  EMBED Equation.3   EMBED Equation.3  hole at x = -2;  EMBED Equation.3   EMBED Equation.3  hole at x = -2 ;  EMBED Equation.3  2. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  g)  EMBED Equation.3   EMBED Equation.3  h)  EMBED Equation.3  3. a)  EMBED Equation.3  b)  EMBED Equation.3   c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3   e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3   g)  EMBED Equation.3 ;  EMBED Equation.3  h)  EMBED Equation.3  4. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h)  EMBED Equation.3  UNIT #8 REVIEW: Combination of Functions 1. Sketch the following functions: i)  EMBED Equation.3  EMBED Equation.3  ii)  EMBED Equation.3  Identify the key properties listed below. Then, sketch the function. a) x-intercept(s) and state number of zeros b) y-intercept c) degree d) end behaviours e) domain f) If you were to complete a finite differences chart, describe the pattern that you would see. 2. Sketch the following functions: i)  EMBED Equation.3  ii)  EMBED Equation.3  Identify the key properties. a) x-intercept b) y-intercept c) increasing/decreasing function d) vertical asymptote e) horizontal asymptote f) end behaviours g) domain and range h) If you were to complete a finite differences chart, describe the pattern that you would see. 3. Sketch  EMBED Equation.3 . Identify the key properties. a) vertical asymptote(s) b) horizontal asymptote(s) c) linear oblique asymptote d) hole(s) e) domain and range f) x-intercept g) y-intercept h) positive and negative intervals i) increasing and decreasing intervals 4. Sketch the following functions: i)  EMBED Equation.3  ii)  EMBED Equation.3  Determine the following: a) amplitude, vertical shift, phase shift and period b) minimum value, maximum value, domain and range c) y-intercept (state exact value if possible; otherwise, state answers accurate to 2 decimal places) d) Determine the x-intercept(s) in one period (state the exact value where possible; otherwise, state answers accurate to 2 decimal places). e) Determine the value of all zeroes. 5. For  EMBED Equation.3  and  EMBED Equation.3 , determine: a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3  (exact answer). e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3  (round to 2 decimal places). 6. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3  (round to 2 decimal places). e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3  (round to 2 decimal places). 7. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3 . e) Determine  EMBED Equation.3 and state the domain. f) Find  EMBED Equation.3 . 8. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d) Find  EMBED Equation.3  (exact answer). e) Determine  EMBED Equation.3  and state the domain. f) Find  EMBED Equation.3  (exact answer). g) Determine  EMBED Equation.3  and state the domain. h) Find  EMBED Equation.3  (exact answer). 9. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d)  EMBED Equation.3  e) Determine  EMBED Equation.3  and state the domain. f)  EMBED Equation.3  10. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d)  EMBED Equation.3  e) Determine  EMBED Equation.3  and state the domain. f)  EMBED Equation.3  11. For  EMBED Equation.3  and  EMBED Equation.3  a) State the domain of  EMBED Equation.3 . b) State the domain of  EMBED Equation.3 . c) Determine  EMBED Equation.3  and state the domain. d)  EMBED Equation.3  e) Determine  EMBED Equation.3  and state the domain. f)  EMBED Equation.3  12. For the given function, determine functions f and g such that  EMBED Equation.3 . a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3   ANSWERS: 1 i)a) -2, 1, 5 (3 zeros) b) 20 c) degree = 4 d)  EMBED Equation.3  e)  EMBED Equation.3  f) QUARTIC: For constant (x, the 4th differences of y are constant. 1 ii)a) -2, -1, 3 (3 zeros) b) -6 c) degree = 3 d)  EMBED Equation.3  e)  EMBED Equation.3  f) CUBIC For constant (x, the 3rd differences of y are constant.  2 i)a) 1 b) 6 c) decreasing d) none e) y = -6 f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h) EXPONENTIAL For constant (x, there is a constant ratio between the 1st differences in y. 2 ii)a) -0.37 b) -2 c) decreasing d) x = -1 e) none f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h) LOGARITHMIC For constant (y, there is a constant ratio between the 1st differences in x.  3.a) x = -1 b) y = 2 c) none d) hole at x = -5 (y-value of hole is 4) e)  EMBED Equation.3 ; EMBED Equation.3  f) 3 g) -6 h) positive:  EMBED Equation.3 ; negative:  EMBED Equation.3  increasing:  EMBED Equation.3 ; decreasing: none 4 i)a) amplitude = 2, vs = 1, ps =  EMBED Equation.3 , period =  EMBED Equation.3  b) min = -1, max = 3,  EMBED Equation.3 ,  EMBED Equation.3  c)  EMBED Equation.3  (2.73) d) One Period:  EMBED Equation.3  e) All zeros:  EMBED Equation.3 4 ii)a) amplitude = 3, vs = -2, ps = - EMBED Equation.3 , period =  EMBED Equation.3  b) min = -5, max = 1,  EMBED Equation.3 ,  EMBED Equation.3  c)  EMBED Equation.3  (-3.5) d) One Period:  EMBED Equation.3  e) All zeros:  EMBED Equation.3  5. a)  EMBED Equation.3  b)  EMBED Equation.3   c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  = -2.13 6. a)  EMBED Equation.3  b)  EMBED Equation.3   c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  = 3.26 e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  = -1.14 7. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 , hole at x = 3;  EMBED Equation.3  f)  EMBED Equation.3  8. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  g)  EMBED Equation.3 ;  EMBED Equation.3  h)  EMBED Equation.3  9. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3  ;  EMBED Equation.3  f)  EMBED Equation.3  10. a)  EMBED Equation.3  b)  EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  11. a)  EMBED Equation.3  b) EMBED Equation.3  c)  EMBED Equation.3 ;  EMBED Equation.3  d)  EMBED Equation.3  e)  EMBED Equation.3 ;  EMBED Equation.3  f)  EMBED Equation.3  12. a)  EMBED Equation.3 ,  EMBED Equation.3  b)  EMBED Equation.3 ,  EMBED Equation.3  c)  EMBED Equation.3 ,  EMBED Equation.3  D41 D42 D43 D44  EMBED Equation.3  D45 D46 D47 D48 D49 D50 D51 D52 x = -1 y = -5 y = 0 x = 3 y =  EMBED Equation.DSMT4  x = 2 x = 3 y = x+9 D53 D54 D55 D56 . D57 D58 . . . 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