9) A) f-1(x) = 8 - x B) f-1(x) = x - 8 C)f-1(x) = x + 8 D) f-1(x) = x 8
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1 Review for Final Eam Name Algebra- Trigonometr MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polnomial completel. If a polnomial cannot be factored, state that it is prime. 1) + - A) ( - )( + ) B) ( + 9)( - ) ( + )( - ) D) prime 1) Evaluate as requested. ) Given that f() = + + 1, find f(-). A) B) 7 - D) - ) Given that f() = +, find f(). A) + 8 B) + + D) + ) ) Determine whether the given function is even, odd, or neither. ) f() = - A) Even B) Odd Neither ) f() = + A) Even B) Odd Neither ) ) ) f() = 8 + A) Even B) Odd Neither ) Find the composite function for the given functions. 7) (g f)(c) when f() = - + and g() = + 9. A) 18c + 7 B) -18c c + 7 D) -18c - 9 7) 8) f g for f() = 7 - and g() = 8) A) + 0 B) D) - 0 Determine whether the given function is one-to-one. If it is one-to-one, find its inverse. 9) f() = 8-9) A) f-1() = 8 - B) f-1() = - 8 f-1() = + 8 D) f-1() = 8 Evaluate the eponential function for the given value. ) f() = - -, f() A) 1 B) 1 D) 1 ) Graph the pair of functions on the same coordinate plane. Use a dashed line for g(). 1
2 11) f() =, g() = - ( + ) + 11) A) B) D)
3 Determine the domain and range of the function from the graph. 1) 1) A) Domain: ( -, ); Range: (-, 0] B) Domain: (-, ); Range: [0, ) Domain: (-, -]; Range: [0, ) D) Domain: (-, -) (-, ); Range: (-, 0) (0, ) 1) 1) A) Domain: [0, ); Range: [0, ) B) Domain: (-, ); Range: [, ) Domain: [, ); Range: (-, ) D) Domain: (-, ); Range: (-, ) Using the given zero, find all other zeros of f(). 1) i is a zero of f() = A) -i,- +, - - B) -i, +, - -i, +, - D) -i, 1 +, 1-1) 1) + i is a zero of f = A) - + i,, and - B) - i,, and - - i, D) - i, - 1) Solve the problem. 1) The number of bacteria growing in an incubation culture increases with time according to n(t) = 00()t, where t is time in das. After how man das will the number of bacteria in the culture be,00? A) 1 da B) das das D) das 1)
4 Solve the equation. 17) (9 - ) = 7 A) 9 B) D) - 17) 18) e - 1 = (e) - 18) A) B) 1-1 D) 0 Evaluate the epression without a calculator. 19) log A) 8 B) 1/ - D) 19) 0) ln e-8 A) B) e ln -8 1 D) -8 0) Evaluate. 1) Let log b A =. and log b B = Find log b A B. A) 0.80 B)..08 D).0 ) Let log b A = 1.1 and log b B = 0.. Find log b AB. A) 1.08 B) D) ) ) Write the epression in epanded form. ) log 9 z A) 9 log log z - log B) log (9 + z) - log 9 log + log z - log D) (log )9 + log z - (log ) ) ) logaz A) (loga) + loga + (logaz) B) loga loga logaz loga + loga + logaz D) loga + loga + logaz ) Solve the equation. ) = A) B) D) ) log 7 = A) 78,1 B),000,000 D) 1,807 ) )
5 Solve the logarithmic equation. 7) ln - ln ( - ) = ln A) 0 B) 9 ln ln - 1 D) 7) Simplif the epression using the product and quotient properties of square roots. Assume that an variables represent positive real numbers. 8) 1 8) A) B) 1 D) 9) - 9) A) - B) - D) - Simplif the epression, leaving our answer with onl positive eponents. Assume that all variables represent positive numbers. 0) (7) 1/ 0) A) B) D) 1) z-/ z/ A) z-1/ B) z1/ z/ D) z/ 1) ) 9/8 /8 ) A) 9/8 B) 1 1/ D) Convert the radical epression to its rational eponent form and then simplif. Assume that all variables represent positive numbers. ) 8 1 A) 1/1/ B) 1 1/81/8 D) 1/1/ ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the correct formula to solve. Round to the nearest cent. A = P(1 + r k )kt or A = Pert ) To get $000 after 11 ears at % compounded semiannuall ) ) What principal invested at.% compounded continuousl for ears will ield $1700? Round the answer to two decimal places. )
6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the length of the arc on the circle of radius r meters intercepted b a central angle θ. Round our answer to three decimal places. ) r = 7, θ = 70 ) A) 8. m B) 9.07 m.8 m D) 7.97 m Graph the function. 7) f() = log ( - 1) 7) A) B) D)
7 8) f() = log 1/ ( + ) 8) A) B) D) Convert the angle from radians to degrees. 9) π 9 A) 00 B) D) 0 9) Convert the angle from degrees to radians. Epress the answer as a multiple of π. 0) 90 A) 9π B) 9π 9 π 18 D) 9π 18 0) 7
8 Find the eact value of the epression. 1) sin 1 1) A) - B) - 1 D) - ) cot 0 ) A) B) - - D) 1 ) csc 10 ) A) - B) - D) Find the amplitude, period, or phase shift of the given function as requested. ) Find the phase shift of = - sin - π ) A) B) - π D) - π ) Find the amplitude of = - cos + π ) A) - π B) π D) - ) Find the period of = cos + π. ) A) π B) π π D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function over a one-period interval. 7) = sin + π 7) 8
9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the eact value of, or state that is undefined. 8) = cos-1 8) A) π B) - π π D) π Use a sketch to find the eact value of. 9) = cos-1 tan - π 9) A) 0 B) - π π D) π Use the fundamental identities and appropriate algebraic operations to simplif the epression. 0) sin (cot + 1) A) cos + 1 B) 1 tan D) -1 0) Find the eact value. 1) Given that cos C = - /1 with C in quadrant II, find cos C. A) B) D) ) ) Given that sin A = -/ with A in quadrant IV, find cos A. A) B) - D) ) Find the eact value b using a half-angle identit. ) cos. ) A) 1 - B) D) Use the given information given to find the eact value of the trigonometric function. ) sin θ = -, θ lies in quadrant IV Find sin θ. ) A) - B) - 0 D) - Complete the identit. ) sin (α + β) + sin (α- β) =? A) cos α cos β B) cos β cos α sin α cos β D) sin α cos β ) Use the given information to find the eact value of the epression. ) Find sin (α + β). tan α = 1 8, α lies in quadrant III, and cos β = - 7, β lies in quadrant II. A) - 87 B) D) 97 ) 9
10 7) Find cos (α + β). sin α = 7 0, α lies in quadrant I, and cos β =, β lies in quadrant I. 9 A) 7 B) D) - 7 7) Solve the triangle. Round the answer to the nearest tenth. 8) 8) 91. ft A) B = 7., b = 8. ft, c =.7 ft B) B = 7., b =.7 ft, c = 8. ft B =.8, b = 8. ft, c =.7 ft D) B = 7., b = 9. ft, c =.9 ft 9) 9) 9 A) a 7., B 7.8, C 1. B) a 8., B.9, C 1.1 a 8., B.8, C 17. D) a 7., B 7.8, C 7.8 Solve the problem. 0) To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. If the distance from the EDM to the towns is. miles and. miles and the angle between the two lines of sight is, what is the distance between the towns? Round our answer to the nearest tenth of a mile. A). mi B). mi.1 mi D).8 mi 0) 1) Two tracking stations are on the equator 1 miles apart. A weather balloon is located on a bearing of N E from the western station and on a bearing of N E from the eastern station. How far is the balloon from the western station? Round to the nearest mile. A) 8 mi B) 7 mi 87 mi D) 78 mi 1)
11 Answer Ke Testname: REVIEW FOR FINAL EXAM 1) A ) D ) A ) A ) B ) B 7) C 8) D 9) A ) A 11) D 1) C 1) D 1) C 1) C 1) B 17) B 18) B 19) C 0) D 1) C ) A ) C ) C ) C ) D 7) B 8) A 9) C 0) D 1) B ) C ) A ) $.79 ) $8.1 ) A 7) C 8) C 9) A 0) D 1) A ) A ) B ) C ) D ) B 11
12 Answer Ke Testname: REVIEW FOR FINAL EXAM 7) 1 -π -1 - π π π π π ) D 9) A 0) B 1) B ) A ) C ) D ) C ) A 7) A 8) A 9) A 0) C 1) B 1
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