MHF 4UI - Final Examination Review

Transcription

1 MHF 4UI - Final Eamination Review Jan 08. If 0, find the possible measure of. tan = cos = (c) sin = 0 (d) cos =. For each function, state the amplitude, period, phase shift, vertical translation, and sketch them. y = sin ( - ) + Amplitude Period Phase shift Vertical translation y = - cos ( - ) Amplitude Period Phase shift Vertical translation. Factor fully: a 8b (c) 4 y 4y 4. Find the family of cubic functions whose -intercepts are -,,. Find the particular member of this family whose graph passes through (-, 40).. Determine the remainder, using the Remainder Theorem, in the division: ( 7 ) ( ) 6. Solve for. Show your work and include i in the final answer. ( C, the comple numbers.) A construction worker drops a bolt while working on a high-rise building 0 m above the ground. After t seconds, the bolt has fallen a distance of s metres, where s(t) = 0 t, 0 t 8. Find the average rate of change during the third second. Find the average rate of change for the interval t 8. (c) Find the rate of change at t =. 8. If f() = 9 8, What is the linear factor of f()? Find the quadratic factor of f(). 9. Find the value of k if there is a remainder of when k is divided by. 0. Find the eact number of degrees in the angles with the following radian measures. (c) (d) 4 Page of

2 . Find the eact radian measure in terms of for each of the following angles. 4 (c) 0 (d) 00. Sketch the graph of the following function. æ y = -cos + p ö ç -,-p p è ø. Solve the following equations: cos 0 cos + sin = 0 (c) sin sin 0 (d) sin sin cos 0 4. Functions R() = and C() = + are the estimated revenue and cost functions for the manufacture of a new product. a) Determine the average profit function AP() = P ( ). Epress this function in two different forms. b) What are the break-even quantities for the profit function?. Find the equation of the horizontal asymptote of each curve. f ( ) = - - g( ) = Let y =. Find the domain, intercepts, and vertical and horizontal asymptotes Then use the information to sketch an approimate graph. Describe behaviour about the asymptotes. 7. The half-life of the isotope Sodium- Na is. seconds. How much of an initial sample of 00 g will be left after minutes? 8. Use squared paper to plot the graph of y log( ) labeling: the -intercept, the vertical asymptote, and two important points. 9. Complete the following chart. Logarithmic Form log log Eponential Form Page of

3 0. Complete the chart. function horizontal asymptote y-intercept growth or decay y y. For the function y ( ) State the equation of the horizontal asymptote. State the Y-intercept. (c) State the domain and range. (d) Sketch the graph on squared paper showing the Y-intercept, the horizontal asymptote, f(-) and f().. Simplify each of the following: (7 y ) 0 (49 ) (c) y y y. The sound level of a moving power lawn is 09 db. The noise level in front of the amplifiers at a concert is about 8 db. How many times louder is the noise at the front of the amplifiers than that of a moving power lawn mower? 4. An earthquake scored.8 on the Richter scale in city A. At city B, it scored.. How much more intense was the earthquake at city B than the earthquake at city A?. Solve for log6 log 8 (c) log ( ) log ( 4) (d) Use your calculator to solve for : 7 7. (Answer to three decimal places) 6. Prove the following identities: sin tan tan cos (c) tan (d) tan sin cos sin (cos ) cos cos cot cot cot 7. Sketch on squared paper y ( )( )( ) by using -intercepts and y-intercepts. Page of

4 8. Neeru is holding a year-end clearance sale in her clothing store. All prices are discounted by %. Write an equation that epresses the sale price of an item as a function of its original price. If the sale price of a shirt is $4, what was its original price? 9. Sketch at least two cycles of the graph of each of the following. y cos y cos (c) y sin 0. Solve each of the following for, R, and graph the solution ( ) 0 ( )( ) 0 (c) Find the equation of the horizontal asymptote of each curve. Then sketch. f () = - - f () = - 4 (c) f () = + -. Find an equation of the oblique asymptote of each curve. Then sketch. Determine the intervals of increase and decrease. f () = h() = - 4 (c) f () = Solve. sin (c) log Page 4 of

5 Answers:., 4 ;, ; 0,, ;, 6 6.,,,;,,,. (4)( 7) ; (a 9 b)(a 9 b) ; ( y )( y ) 8 4. y k( )( ) ; y ( )( ) ;, i m / s, m / s; 0m / s 8. ( 4); ,, 900, 660.,,, Graphing Calculator. k, k, k I; k, k, k, k I; k, k I; k, k, k, k I aka ;, 0.. y ; y 0 6. Graphing Application % 0.09g 8. Graphing Application 9., log,, log y, (0,4), growth; y,(0, ), decay. y ; (0,); D R, R y, y R; Graphing App. 49 0,, y times 8 (..8) times. 64; 64; ; All QED 7. Graphing App 8. S( p) 0.7 p; $ 6 9. Graphing App 0. 0 ; [,]; or. H.A.: y ; y 0; y. Graphing App. O.A.: y 4; y ; y. Graphing App.,.9 (.9, ), (.9,0) (0,.9); (,.9) (0, ), (.9,0); all. Graphing App. Page of