C)not a function. B) function domain: {-3, 2, 4, 6} range: {-7, 4, 2, -1}

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1 Name Spring Semester Final Review (Dual) Precalculus MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation represents a function. If it is a function, state the domain and range. 1) {(-3,-7),(, ), (, ), (6,-1)} A) function domain: {-7,,, -1} range: {-3,,, 6} B) function domain: {-3,,, 6} range: {-7,,, -1} C)not a function 1) Find the domain of the function. ) f() = 1 - A) { 1} B) { 1} C){ 3} D) { 3} ) The graph of a function f is given. Use the graph to answer the question. 3) Use the graph of f given below to find f(0). 3) A) 0 B) 0 C)70 D) 0 The graph of a function is given. Decide whether it is even, odd, or neither. ) 8 6 ) A) even B) odd C) neither 1

2 Determine algebraicall whether the function is even, odd, or neither. ) f() = -3 A) even B) odd C) neither ) 6) f() = A) even B) odd C) neither 6) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 7) (0, 1) 7) - - A) increasing B) decreasing C) constant SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function. 8) 1 if 0 < 6 f() = if 6 < 9 3 if 9 1 8)

3 Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 9) f() = -( + 1) + 9) ) f() = ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the correct function to the graph. 11) 11) A) = B) = C) = - D) = 1-3

4 Suppose the point (, ) is on the graph of = f(). Find a point on the graph of the given function. 1) The reflection of the graph of = f() across the -ais A) (-, -) B) (, ) C)(-, ) D) (, -) 1) Use factoring to find the zeros of the quadratic function. List the -intercepts of the graph of the function. 13) F() = A) = -, = - B) =, = - C) =-, = D) =, = 13) Find the verte and ais of smmetr of the graph of the function. 1) f() = + - A) (-, 9); = - B) (,-9); = C)(, 9); = D) (-,-9); = - 1) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function using its verte, ais of smmetr, and intercepts. 1) f() = - 0 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 16) f() = A) minimum; - 1 B) maimum; - 8 C)minimum; - 8 D) maimum; ) 17) f() = A) minimum; - B) minimum; - 1 C)maimum; - 1 D) maimum; - 17) Find the zeros of the quadratic function using the Square Root Method. List the -intercepts of the graph of the function. 18) (- 7) - = 0 A) = 3 B) = -, = C) = -1, = D) =, = 1 18)

5 Find the real zeros, if an, of each quadratic function using the quadratic formula. List the -intercepts, if an, of the graph of the function. 19) g() = A) =, = 1 B) = + 8 C) = ± 8 D) No real zeros or -intercepts 19) Find the zeros of the quadratic function b completing the square. List the -intercepts of the graph of the function. 0) f() = A) = 1, = 13 C) = - 1, = - 13 B) = - 13, = 13 D) = - 1, = ) Find the real zeros of the function. List the -intercepts of the graph of the function. 1) F() = - + A) = -, = B) = -1, = 1, = -, = C) = -, = D) = -, = 1) Solve the inequalit. ) A) (-, 3] B) [3, ] C)[, ) D) (-, 3] or [, ) ) 3) A) (-, -6] or [0, ) B) [0, 6] C)(-, 0] or [6, ) D) [-6, 0] 3) Solve the problem. ) A projectile is thrown upward so that its distance above the ground after t seconds is h = -11t + 6t. After how man seconds does it reach its maimum height? A) 31. s B) s C)1 s D) s ) The number of mosquitoes M(), in millions, in a certain area depends on the June rainfall, in inches: M() = 3 -. What rainfall produces the maimum number of mosquitoes? A) 3 in. B) 9 in. C)0 in. D) 1. in. ) ) Find the comple zeros of the quadratic function. 6) h() = A) = i B) = -7-9i, = i C) = -, = - D) = i, = -7-3i 6) Without solving, determine the character of the solutions of the equation. 7) = 0 A) a repeated real solution B) two unequal real solutions C) two comple solutions that are conjugates of each other 7)

6 8) = 0 A) two comple solutions that are conjugates of each other B) a repeated real solution C) two unequal real solutions 8) Solve the equation. 9) = 11 A) {17, } B) {-, } C){-1, } D) {-1, } 9) Solve the problem. 30) + 6i is a zero of a quadratic function with real coefficients. Find the other zero. A) 11 B) 6i - C) - - 6i D) - 6i 30) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the inequalit. Epress our answer using interval notation. Graph the solution set. 31) k ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the -intercepts to find the intervals on which the graph of f is above and below the -ais. 3) f() = ( + )3 A) above the -ais: no intervals B) above the -ais: (-, ) below the -ais: (-, -),(-, ) below the -ais: (-, -) C)above the -ais: (-, -), (-, ) below the -ais: no intervals D) above the -ais: (-, -) below the -ais: (-, ) 3) Find the domain of the rational function. 33) g() = A) { -3, 3, -8} B) all real numbers C){ -3, 3} D) { 0, 9} 33) Find the vertical asmptotes of the rational function. 9 3) f() = ( + 6)( - ) A) = -9 B) = -6, =, = -9 C) = -6, = D) = 6, = ) R() = + - A) = - B) = -6, =, = -3 C) = 6, = - D) = -6, = 3) 3) 6

7 Use the graph to find the vertical asmptotes, if an, of the function. 36) 36) A) = B) =, = 0 C) = D) =, = Give the equation of the horizontal asmptote, if an, of the function. 37) f() = A) = -3, = 3 B) = 1 C) = 0 D) no horizontal asmptotes 37) 38) g() = A) = 0 B) = 1 C) = 7 D) no horizontal asmptotes 38) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the inequalit. Epress our answer using interval notation. Graph the solution set. 39) k > 9 39) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 0) f() = A) No; the last term has no variable B) Yes; degree 3 C)Yes; degree 6 D) Yes; degree 0) Use snthetic or long division to perform the division. 1) ) A) B) C) D)

8 Use the remainder theorem and snthetic division to find f(k). ) k = -3; f() = A) 33 B) - C)36 D) -10 ) Use snthetic division to decide whether the given number is a zero of the given polnomial. 3) ; f() = A) Yes B) No 3) ) 7i; f() = A) Yes B) No ) Form a polnomial whose zeros and degree are given. ) Zeros: -3, -1, ; degree 3 A) f() = for a = 1 B) f() = for a = 1 C)f() = for a = 1 D) f() = for a = 1 ) For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 6) f() = ( - 3)( + 3)3 6) A) 3, multiplicit 1, touches -ais; -3, multiplicit 3 B) 3, multiplicit 1, crosses -ais; -3, multiplicit 3, crosses -ais C) -3, multiplicit 1, touches -ais; 3, multiplicit 3 D) -3, multiplicit 1, crosses -ais; 3, multiplicit 3, crosses -ais SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function. ( + 3)( + ) 7) f() = )

9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 8) Decide which of the rational functions might have the given graph ) A) R() = C)R() = ( + )( - 3) + ( - )( + 3) B) R() = D) R() = - ( + )( - 3) - ( + )( - 3) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function. 9) f() = + 9 9) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the equation of the oblique asmptote, if an, of the function. 0) f() = A) = 0 B) = + 1 C) = - 1 D) = 0) Solve the inequalit. 1) (- 1)( - ) > 0 A) (1, ) B) (, ) C)(-, 1) or (, ) D) (-, 1) 1) 9

10 ) - 0 A) [-, 0] B) (-, -] or [0, ) C)(-, 0] or [, ) D) [0, ] ) Use the Factor Theorem to determine whether - c is a factor of f(). 3) f() = ; + 9 A) Yes B) No 3) Give the maimum number of zeros the polnomial function ma have. Use Descarte's Rule of Signs to determine how man positive and how man negative zeros it ma have. ) f() = A) ; 3 or 1 positive zeros; 3 or 1 negative zeros B) ; or 0 positive zeros; 3 or 1 negative zeros C); or 0 positive zeros; or 0 negative zeros D) ; 3 or 1 positive zeros; or 0 negative zeros ) List the potential rational zeros of the polnomial function. Do not find the zeros. ) f() = A) ± 1 6, ± 1 3, ± 1, ± 3, ± 1, ± B) ± 1, ± 3, ± 1, ±, ± 3, ± 6 ) C)± 1 6, ± 1 3, ± 1, ± 1, ± D) ± 1 6, ± 1 3, ± 1, ±, ± 1, ±, ± 3 3 Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 6) f() = A) ; f() = ( - )( + 1) B) -, ; f() = ( - )( + )( + 1) C) -1, 1; f() = ( - 1)( + 1)( + ) D) -, -1,, 1; f() = ( - )( + )( - 1)( + 1) 6) Solve the equation in the real number sstem. 7) = 0 A) {3, } B) {-,-3,-1} C){1, 3, } D) {-,-3} 7) 8) = 0 A) {-6, 6} B) {-6,-,, 6} C){-, } D) {-1, 1} 8) Information is given about a polnomial f() whose coefficients are real numbers. Find the remaining zeros of f. 9) Degree 3; zeros: 3, - i 9) A) + i B) - + i C) -3 D) no other zeros Form a polnomial f() with real coefficients having the given degree and zeros. 60) Degree 3: zeros: 1 + i and - A) f() = B) f() = C) f() = D) f() = )

11 Use the given zero to find the remaining zeros of the function. 61) f() = - 1-6; zero: -i A) i, i, -i B) i, 8, -8 C)i,, - D) i, 8i, -8i 61) Evaluate the epression using the values given in the table. 6) (f g)() 6) f() g() A) 3 B) C) 11 D) Undefined Find the inverse of the function and state its domain and range. 63) {(7, -8), (, -7), (3, -6), (1, -)} A) {(-7, -8), (-8, 3), (7, ), (-7, -6)}; D = {(-7, -8, 7}; R = {(-8, 3, -6} B) {(-7, -8), (-, 3), (7, 3), (-7, -6)}; D = {-7, -, 7}; R = {-8, 3, -6} 63) C) 7, - 1 8,, - 1 7, 3, - 1 6, 1, - 1 ; D = { 7,, 3, 1}, R = - 1 8,- 1 7, - 1 6, - 1 D) {(-8, 7), (-7, ), (-6, 3), (-, 1)}; D = {-8, -7, -6, - }; R = {7,, 3, 1} SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 6) f() = + 6) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether or not the functions are inverses of each other. 6) f() = + 16, g() = 1-6) A) No B) Yes 11

12 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use transformations to graph the function. Determine the domain, range, and horizontal asmptote of the function. 66) f() = ) ) f() = ) Graph the function. 68) f() = 3 68)

13 69) f() = -1 + e 69) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 70) 1 + = 6 A) {} B) {16} C){-1} D) {1} 70) 71) 3- = ) A) {-} B) 1 C) 1 7 D) {} 7) e - 1 = (e) - A) 1 B) {0} C) 3 D) 1 6 7) Change the eponential epression to an equivalent epression involving a logarithm. 73) 6 3 = 16 A) log 16 = 6 3 B) log 16 = 3 6 C) log 6 = 3 16 D) log 3 = ) 7) 3/ = log A) log 3 = 3 B) log 3 = C) log 3 = D) log 3 = 7) Find the eact value of the logarithmic epression. 7) log ) log 8 1 A) -8 B) 8 C) - D) 7) 76) A) 1 8 B) 8 C)1 D) 0 13

14 77) log ) A) 1 B) 1 8 C)8 D) 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function. 78) = log 1/ 78) - - Use transformations to graph the function. 79) Use the graph of log to obtain the graph of f() = -1 + log. 79) Use transformations to graph the function. Determine the domain, range, and vertical asmptote of the function. 80) h() = 3 + log( + ) 80)

15 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 81) log 3 7 = A) {9} B) {3} C){81} D) {30} 81) 8) log ( + 1) = -1 8) A) - B) 6 C) 6 D) - 83) ln = 1 A) ln 3 B) e 3 C){e /3 } D) 3 ln 1 83) Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. 8) log. A) 0.18 B) C). D) 6 8) 8) log 70 + log ) A) 1 B) 7 C) D) 70 86) log 16 - log 8 86) A) 8 B) C)1 D) 16 Write as the sum and/or difference of logarithms. Epress powers as factors. 87) log ) A) log 13 - log log 13 B) log 13 (6 ) - log 13 C) log log 13 m log 13 D) log log 13 - log 13 88) log 3 8 qp 88) A) 1 8 log 3 - log 3 q - log 3 p B) log 3 - log 3 q - log 3 p C)8 log 3 - log 3 q - log 3 8 D) 1 8 log 3 - log 3 q - log 3 p 1

16 Epress as a single logarithm. 89) 9log c + 6log c 89) A) log c ( ) B) log c 9 log c 6 C) log c 9 6 D) log c 96 90) 3log 6 + log 6 ( - 6) A) log 6 ( - 6)1 B) log 6 3( - 6) C) log 6 ( - 6) D) 1 log 6 ( - 6) 90) Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to three decimal places. 91) log ) 6 A) 1.60 B) C) 1.76 D) 0.78 Solve the equation. 9) log3 + log3( - ) = A) {3} B) No real solutions C){-3, 7} D) {7} 93) log ( + 1) = 1 + log ( - 3) A) B) - 1 C) 1 D) - 9) 93) 9) (7-3) = 1 9) A) 1 B) {1} C){-3} D) {3} Solve the eponential equation. Epress the solution set in terms of natural logarithms. 9) 3 6 =.3 6 ln.3 A) ln 3 B).3 ln 6 ln 3 C) ln.3 3 ln 6 D) ln.3 6 ln 3 9) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 96) = A) {-.7} B) {1.7} C){-0.6} D) {6.79} 96) 97) e = 3 A) {0.} B) {1.63} C){.9} D) {0.} 97) Solve the problem. Round our answer to three decimals. 98) How long will it take for an investment to double in value if it earns 8.7% compounded continuousl? A) ears B) 1.6 ears C) 7.9 ears D) 8. ears 98) 16

17 Solve the problem. 99) How long does it take $11 to triple if it is invested at 7% interest, compounded quarterl? Round our answer to the nearest tenth. A) 1.8 months B) 1.8 ears C) 18.1 months D) 18.1 ears 99) 0) The half-life of silicon-3 is 7 ears. If 0 grams is present now, how much will be present in 900 ears? (Round our answer to three decimal places.) A) B) C) 0 D) ) 1) The size P of a small herbivore population at time t (in ears) obes the function P(t) = 800e0.t if the have enough food and the predator population stas constant. After how man ears will the population reach 1600? A). rs B) 3.7 rs C)8.7 rs D) 33. rs 1) Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. ) a = ; d = 8 ) an =?; a16 =? A) an = + 8n; a16 = 8 B) an = + 8n; a16 = 130 C)an = - 8n; a16 = 130 D) an = + 8n; a16 = 130 Find the sum of the arithmetic sequence. 3) (-6) + (-1) A) 330 B) 170 C)160 D) 16 3) Determine whether the sequence is geometric. ), 1, 36, 8, 3,... A) Geometric B) Not geometric ) Find the nth term of the geometric sequence. ) a = 3; r = -3 A) an = 3 3n-1 B) an = 3-3n-1 C)an = 3-3n D) an = -3 3n-1 ) 6),, 1, 1, 1 6) A) an = 1 n B) an = 1 n-1 C)an = 1 n-1 D) an = 1 n + 1 Find the sum. 7) k=1 3 () k A) B) 6 3 C) 86 3 D) ) 17

18 Find the sum of the infinite geometric series. 8) A) B) 8 C)6 D) 8) 9) 3 k=1 k-1 9) A) 8 3 B) 1 C)16 D) Find the sum of the arithmetic sequence. 1) A) 1168 B) 167 C) 10 D) ) Solve the equation. 111) - = A) {-, 6} B) {-6, 6} C){, -6} D) 111) 11) + 3 = - 3 A) {6, 13} B) {1, 6} C){6} D) {1, 13} 11) 113) = 1 A) {3} B) {3,-1} C){-3, -1} D) 113) Evaluate the epression. 9 11) 7 A) 18 B) 36 C)1 D) 7 11) Find the indicated coefficient or term. 11) The 3rd term in the epansion of ( + )3 A) 8 B) C)96 D) 96 11) 116) The 8th term in the epansion of ( + 3)11 A) 71,77 B) 0,707 C) 0,708 D) 71,77 116) Epand the epression using the Binomial Theorem. 117) ( + 9) A) ,80 + 3, B) , C) ,80 + 9,09 D) ,80 + 3,80 + 9,09 117) 18

19 118) ( - )3 A) B) C) D) ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the verte, focus, and directri of the parabola. Graph the equation. 119) ( - 1) = -8( + ) 119) Graph the equation. 10) (- ) + ( + 1) 9 = 1 10) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the partial fraction decomposition of the rational epression ) (- )( - ) A) B) C) D) ) 1) ( + 1)( - 1) A) C) B) D) ) 19

20 + 13) A) ( - 1) C) ( - 1) B) ( - 1) D) ( - 1) 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the hperbola. 1) (- 1) - ( - 1) 16 = 1 1)

21 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 1) B ) B 3) B ) A ) B 6) C 7) B 8) (9, 9) (6, 6) (0, 1) (9,.1) (6, 1) (1,.) - 9) ) ) A 1) C 13) B 1

22 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 1) D 1) verte (, -) intercepts (0, 0), (, 0) ) C 17) D 18) D 19) C 0) C 1) B ) D 3) B ) C ) D 6) D 7) B 8) A 9) C 30) D 31) [- 17, 1 ] 3) B 33) C 3) C 3) D 36) A 37) C 38) D ) (-, - 3 ) (, ) 0) B 1) D ) D

23 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 3) A ) A ) A 6) B 7) ) B 9) ) C 1) C ) D 3) A ) D ) A 6) B 7) B 8) A 9) A 60) D 61) C 6) A 63) D 3

24 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 6) ) B 66) domain of f: (-, ); range of f: (-, ); horizontal asmptote: = 67) domain of f: (-, ); range of f:(3, ) horizontal asmptote: = 3

25 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 68) ) ) D 71) D 7) D 73) B 7) B 7) C 76) D 77) D 78) - -

26 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 79) ) = domain (-, ) range (-, ) vertical asmptote = - 81) B 8) A 83) C 8) C 8) A 86) C 87) D 88) A 89) D 90) B 91) C 9) D 93) A 9) D 9) D 96) A 97) D 98) C 99) B 0) D 6

27 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 1) B ) B 3) D ) A ) B 6) C 7) B 8) B 9) B 1) C 111) C 11) C 113) B 11) B 11) A 116) D 117) C 118) C 119) verte: (-, 1) focus: (-, 1) directri: = ) ) B 1) C 13) D - 7

28 Answer Ke Testname: PRECAL SPRING SEMESTER FINAL EXAM AHS 1)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Practice for the Final Eam MAC 1 Sullivan Version 1 (2007) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the distance d(p1, P2) between the points