1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)

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1 Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( ) c. ( b ) f ) b.). Evaluate the function at each specified value of the independent variable and simplify. f ) ( c.) f () b. f () c. f (0) d. (). Find the domain of the given function. Use interval notation! ( ) f b. g ( ) c. f ( ) 6 f ) b.) c.) d.) ) b.) c.) 4. Use a graphing utility to graph the function and determine the open intervals on which the function is increasing, decreasing, or constant (use interval notation!). Identify any relative minimum or relative maimum values of the function. f ( ) b. f ( ) 9 4) increasing: decreasing: constant: rel. min.: rel. m: 4b.) increasing: decreasing: constant: rel. min.: rel. m:. Determine algebraically if the function is even, odd, or neither. Verify using a graphing utility. ( ) f 6 b. f ( ) 6 4 c. f ( ) ) b.) c.)

2 6. Given f ( ), g ) f ( ), g( ), or h() to () ( and h ) j. j ( ) ( ) 6 b. ( ) (. Describe the sequence of transformations from j c. j ( ) 7 ) b.) c.) 7. Given f ( ), g( ) and h ( ). Find the indicated values. ( f g)(4) b. ( f h)() c. ( fh )() 7) 7b.) g h d. e. ( f )( ) 7c.) g f. ( f h)( 4) 7d.) 7e.) 7f.). Find the inverse of the function algebraically. 7 f ( ) b. f ( ) 4 c. f ( ) 0 ) b.) 9. Show that f () and () g are inverses. c.) f ( ), g ( ), 0 0. Given the graph f () y at the right, sketch the following: y b. y f () c. y f ( ) d. y f () f ( )

3 Chapter : Polynomials and Rational Functions. Epress each comple number in standard form a bi. 4 b. i c. 4 7i ) b.) c.) d. i i e. i f. 4i i i 4 d.) e.). Solve the following equations for. f.) b. 4 7 c If P ( ) 4, use synthetic substitution to find: P () b. P c. (i) ) b.) c.) P ) b.) c.) 4. If - is a zero of the polynomial P( ) k, find the value of k. 4.). A polynomial () P is divided by. The quotient is and the remainder is -. Find () P..) 6. Two roots of the equation are and. Find the remaining roots. 6.) 4 7. Find all real zeros of f ( ) Use the rational root theorem and synthetic division. 7.)

4 . Sketch the graph of the equation (without a graphing calculator). Use the zeros of the function and the end behavior of the function. f ( ) ( )( ) 9. A rectangular enclosure, sub-divided into three congruent pens as shown, is to be made using a barn as one side and 0 meters of fencing for the rest of the enclosure. Find the value of that gives the maimum area for the enclosure. 9.) BARN 0. Solve for ) 4. Find all real and imaginary roots of ). Find a cubic equation with integral coefficients having the solutions i, and..). Graph if f ( ) if if - -

5 4. Sketch the graph of the rational function by hand. Identify any -intercepts, the y-intercept, horizontal asymptotes, vertical asymptotes, and slant asymptotes. ( ) f -intercept(s) = y-intercept = H.A. = V.A. = S.A. = b. ) 4 f -intercept(s) = ( y-intercept = H.A. = V.A. = S.A. = c. ( ) f -intercept(s) = y-intercept = H.A. = V.A. = S.A. =. Determine whether y y 6 has symmetry in: Circle the correct answer (s) the -ais b. the y-ais c. the line y= d. the origin 6. Sketch the graph of the quadratic function. Identify the verte & intercept(s). f ( ) ( 4) 4 verte = -intercept(s) = y-intercept =

6 Chapter and Eponents Packet (Ch from other tetbook): Eponential Functions and Logarithmic Functions 7. Evaluate the following eponential epressions: 0 0 b. 4 4 c. 9 d ) 7b.) 7c.) 7d.). Solve each eponential equation: 7 b. 4 ) b.) 9. A gallon of gasoline cost $.09 two years ago. Now it costs $.7. To the nearest percent, what has been the annual rate of decrease in cost? 9.) 0. Graph y and y How are the graphs related? on the same set of aes.. Suppose $,00 is invested at an interest rate of 9.6%. how much is the investment worth after years if interest is compounded: Monthly? b. Continuously? ) b.)

7 . Given log, using rules of logarithms, find the value of: {without a calculator!} log b.. log ) b.). Find the eact value of: without a calculator! log 6 b. log 7 c. log 4 64 ) b.) 4. Epress the following in terms of log M and log N b b c.) log M N b b. log M N b 4) 4b.). Solve log log..) 6. Solve to the nearest hundredth. 6.) 7. If 0 mg of ibuprofen has a half-life of hours, then how much ibuprofen is in a person s bloodstream after (a) 7 hours? (b) after t hours? 7) 7b.). Simplify: ) b. 7 b.) c. 6 4 c.)

8 9. Solve for : 4 9) log b. log log 4 9b.) c. log 9c.) d. log6 4 log6 log6 9d.) 40. Solve for : e 40) b. 6 40b.) c. e e 0 40c.) 9 7 d. 40d.)

9 Chapter 4 [4.-4.6]: Trigonometry 4. A circle has a radius of 7 inches. Find the length of the arc intercepted by a central angle of ) 4. The circular blade on a saw rotates at 400 revolutions per minute. Find the angular speed in radians per second. 4) b. The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second. 4b.) 4. A satellite in circular orbit km above a planet makes one complete revolution every 0 minutes. Assuming that he planet is a sphere of radius 6400 km, find the linear speed of the satellite in kilometers per minute. Round your answer to the nearest whole number. 4.) 44. A truck is moving at a rate of 90 km per hour and the diameter of its wheels is. meters. Find the angular speed of the wheels in radians per minute. 44.) 4. Evaluate (if possible) the si trigonometric functions if. 4. sin cos tan csc sec cot 46. Evaluate the trigonometric function. sin 4 7 b. csc 6 c. tan 46) 46b.) 46c.) sec e. cot d. 4 f. cos 4 46d.) 46e.) 46f.)

10 47. Find the eact values of the si trigonometric functions of the angle shown in the figure. sin csc 47. cos sec tan cot 4. Simplify each epression. sin cos cos sin cos sin cos 4) b. 4b.) tan c. sec d. sec sin tan 4c.) 4d.) 49. Find two solutions of the equation. Give your answers in degrees 0 60 and radians 0 without using a calculator. cot b. sec 49) 49b.)

11 0. John stands 0 meters from a water tower and sights the top at an angle of elevation of 6. How tall is the tower? 0.). The Aerial run in Snowbird, Utah has an angle of elevation of 0.. Its vertical drop is 900 feet. Estimate the length of the run..). In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a passenger estimates the angle of elevation to the top of the falls to be 0. If the Horseshoe Falls are 7 feet high, what is the distance from the boat to the base of the falls?.). Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. cos, sin 0. 7 sin cos tan csc sec cot 4. The point is on the terminal side of an angle in standard position. Determine the eact values of the si trigonometric functions of the angle., sin csc 4. cos tan sec cot

12 Answer the questions regarding the amplitude, period, phase shift and vertical shift of each trigonometric function y a cosb c d or y asin b c d. Then graph two full periods of the trigonometric function. Be sure to label your aes accurately!. y cos4 a = b = c = d = amplitude = period = phase shift = vertical shift = 6. y sin a = b = c = d = amplitude = period = phase shift = vertical shift = 7. y cos 4 a = b = c = d = amplitude = period = phase shift = vertical shift =

13 . y 4cos a = b = c = d = amplitude = period = phase shift = vertical shift = Graph two periods of the trigonometric function. 9. y tan a = b = c = d = amplitude = period = phase shift = vertical shift = 60. y cot a = b = c = d = amplitude = period = phase shift = vertical shift =

14 Answer Key Midterm Review Packet January 0 0 b. c. b 6 -,, b., c., 4 4, 4 increasing:,, 4 decreasing:, 4 constant: none 4 rel. min.:, 4 rel. m:, 4b. increasing:, 4b. decreasing:, 4b. constant: none 4b. rel. min.:, 0 ;, 0 4b. rel. m: none even b. neither c. odd 6 f () has a horizontal shift units left, reflects over the -ais and has a vertical shift 6 units down 6b. f () has a vertical stretch of and a vertical shift up units 6c. f () has a horiz. shift units right, reflects over the -ais, a vertical shrink of ½ and a vertical shift 7 units down 7-7 7b. 70 7c. 7d. 7e. 7 7f. -97 ( ) f 7 b. f ( ) c. f ( ) 0, show that f g( ) g f ( ) 0. See graphs i b. i c. 4 7 i 6 6 d. 4 i e. i f. 7 i 4, b. c. i b. 4 b. - c. d. 6 c. 4i P ( ) 4,,, 6. i 7.. See graph 9. meters 0.,.,, i. f ( ) 6. See graph 4 -intercept:, 0 ; y-intercept: 0, ; H.A.: y = ; V.A.: = ; S.A.: none 4b. -intercept: 0, 0; y-intercept: 0, 0; H.A.: y = ; V.A.: = and = -; S.A.: none 4c. -intercept: none; y-intercept: ; H.A.: none; V.A.: = ; S.A.: + 0,, 4, 0 ; 6, 0 0,. c and d 6. verte: 4 ; -intercept: ; y-intercept: 7 7 7b. - b c. 79 7d % 0. See graph $4.9 b. $ b b. 4b. log M log N. b t b c. 4 logb M logb N b. y 0 b. 64 c. 40c., 0.69(ln) 9 9b., 9c b d. 0 40d. - inches 4 0 rad/sec 4b. 00in/sec km/min rad/min 4. sin cos tan csc sec cot 46

15 46b. - 46c. 46d. 46e. 0 46f. 47. sin cos tan csc sec cot 4 cot 4b. 4c. sec 4d. cos 49 0, 00,, 49b. 7 4,,, meters. 9.4 feet feet sin. sin csc csc See graphs 7 0 cos 7 sec 7 cos 7 sec 7 tan 0 cot 0 0 tan. a = b = 4 c = 0 d = - Amp = Per = 6. a = - b = 7. a = b = c = cot Phase Shift = 0 Vert. Shift = - c = 0 d = Amp = Per = 4 Phase Shift = 0 Vert. Shift = d = 4 Amp = Per = Phase Shift = Vert. Shift = 4. a = 4 b = c = - d = - Amp = 4 Per = 4 Phase Shift = - Vert. Shift = - 9. a = - b = c = 0 d = 0 Amp = none Per = Phase Shift = none Vert. Shift = none 60. a = b = c = 0 d = Amp = none Per = Phase Shift = none Vert. Shift =