MAT 800 FINAL EXAM HOMEWORK Read te directions to eac problem careully ALL WORK MUST BE SHOWN DO NOT USE A CALCULATOR Problems come rom old inal eams (SS4, W4, F, SS, W) Solving Equations: Let 5 Find all numbers, any, suc tat Let and g 6 Find all numbers, any, suc tat g Solve te equation 4 Solve te equation Finding Domain o Functions: 5 Find te domain o te unction 6 Find te domain o te unction 7 Find te domain o te unction 8 Find te domain o te unction 9 Find te domain o te unction Graping Piece-wise Functions: 0 Sketc a grap o te unction Sketc a grap o te unction Sketc a grap o te unction log 7e log log 4 5 State your answer in interval notation 5 State your answer in interval notation State your answer in interval notation 6 State your answer in interval notation log ln State your answer in interval notation 9 4 g 0 0 4 g 4 4 0 0 4 Sketc a grap o te unction g
4 Sketc a grap o te unction g 0 0 Inverse Functions: 5 Let log4 5 Find 5 9 0 4 7 4 6 Let Find 7 Let Find 8 Let Find 9 Let Find Graping Polynomials: 0 Grap te polynomial p Grap te polynomial p 50 5 4 5 0 4 Grap te polynomial 5 Grap te polynomial p p p 4 Grap te polynomial Composition o Functions & Evaluating Functions: 5 Let 7 4 and g 5 completely (a) g 6 Let Find 6 7 Let e and g 8ln is te inverse unction o is te inverse unction o is te inverse unction o is te inverse unction o is te inverse unction o, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts Find eac o te ollowing and simply your answers and simply your answer completely Find and simply eac o te ollowing (a) g g 8 Let Find a a and simply your answer completely
4 4 Find and g 7 log 9 Let 0 0 Let a a g Find and simply and simply your answer completely Let and g g g Find and simply g 4 Let and g Find and simply g5 Let a a Find Ma/Min Story Problems: and simply your answer completely 4 A stone is launced o o a building wic is 95 eet ig Its eigt at time t is given by te unction t 950t 4t were time is measured in seconds and eigt is measured in eet At wat time does te stone reac its maimum eigt? Wat is te maimum eigt? 5 A ball is catapulted upwards Its eigt at time t is given by 40 t 6t t were time is measured in seconds and eigt is measured in meters Wat is te maimum eigt te ball will reac? Zeros o Polynomials: 6 6 Find all te zeros o te polynomial 0 te orm a bi 7 Given tat i p p 4 is a zero o te polynomial 8 zeros Please epress any non-real zeros in te orm 5 a bi 8 8 Find all te zeros o te polynomial 5 te orm a bi 4 9 Find all te zeros o te polynomial p te orm a bi p Please epress any non-real zeros in 45 40 Find all te zeros o te polynomial p 4 4 zeros in te orm a bi, ind and list all oter Please epress any non-real zeros in Please epress any non-real zeros in Please epress any non-real Graping Rational Functions: 4 Grap te unction 5 4, labeling all intercepts and asymptotes 4
4 Grap te unction 4 Grap te unction 44 Grap te unction 45 Grap te unction Modeling wit Functions:, labeling all intercepts and asymptotes 6, labeling all intercepts and asymptotes 5, labeling all intercepts and asymptotes 9 4, labeling all intercepts and asymptotes 6 9 46 A piece o wire inces long is bent into te sape o an equilateral triangle Find a unction o tat represents te area o te triangle and state te domain o te unction 47 A cardboard bo as a square base and a square top Te eigt o te bo is inces Epress te surace area A (te sum o te areas o all si sides o te bo) in terms o te lengt l o te bo 48 A crate as a eigt o 6 eet Te sum o te areas o all 6 sides o te crate is 40 square eet Epress te lengt l o te crate in terms o te widt w (ie write l as a unction o w) Evaluating Logaritms: ln5 log 49 Find te eact value o te epression log 5 65e
ln e e ln 5 Find te eact value o te epression e ln e log 8 5 4 ln6 5 Find te eact value o te epression 4 ln e log ln6 50 Find te eact value o te epression 5 e 5 Find te eact value o eac epression: (a) log log 4 Solving Logaritmic & Eponential Equations: 6 ln 7 e 6 log 5 log 54 Find all values o, any, suc tat 55 Find all values o, any, suc tat log log 8 log 4 0 00 56 Solve te equation 7 log 57 Find all values o, any, suc tat log 58 Find all values o, any, suc tat e e 59 Find all values o, any, suc tat log4 8 log4 8 Graping Logaritmic & Eponential Functions: 60 Grap te unction ln e 6 Grap te unction 6 Grap te unction 6 Grap te unction log 64 Grap te unction Eponential Function Applications:, labeling all intercepts and asymptotes 7, labeling te y-intercept and any asymptotes 5, labeling te y-intercept and any asymptotes, labeling all intercepts and asymptotes log P t 00e 65 Te general unction, labeling all intercepts and asymptotes is used to model te number o bacteria in a culture P 00 0 is te initial population and t is time measured in ours Suppose te bacteria culture reaces 00 ater 5 ours How long will it take or te bacteria culture to triple in size? Simply your answer as muc as possible P t 640e 66 Te general unction is used to model a dying bird population P 640 is te initial population and t is time measured in days Suppose te bird population was reduced to one quarter o its initial size ater 9 days How long will it take beore tere are only 40 birds let in te population? Simply your answer as muc as possible 0 67 Te general unction P t P0 e is used to model an insect population P 0 is te initial population ( P 0) and t is time measured in ours Suppose te insect population tripled ater 7 0
ours How long will it take te insect population to grow to nine times its initial size? Simply your answer as muc as possible n t n0e 68 Te general unction is used to model te number o bacteria in a certain culture te time t is measured in ours Suppose te culture initially contains,000 bacteria Ater two ours te bacteria count is 8,000 Find te eact time it took or te bacteria count to triple n t n0e 69 Te general unction is used to model te number o bacteria in a certain culture n 0 is te initial population and t is time measured in ours Suppose te culture initially contains 80 bacteria and ater 5 ours te bacteria count decreases to 60 Wat would you epect te size o te culture to be ater 0 ours? Simply your answer Trigonometric Evaluation Problems: 70 Find te eact value o eac trigonometric unction at te given real number, it eists (a) cos csc 7 Find te eact value o eac trigonometric unction at te given real number, it eists 7 6 (a) sin cot 6 7 Find te eact value o eac trigonometric unction at te given real number, it eists (a) tan sin 7 Find te eact value o 05 74 Find te eact value o cos 5 4 sec 75 Find te eact value o eac trigonometric unction at te given real number, it eists (a) csc sin 76 Find te eact value o 75 cot 7 77 Find te eact value o eac trigonometric unction at te given real number, it eists 0 9 (a) cos sec Graping Trigonometric Functions: 78 Find and state te amplitude and period lengt or te unction 4cos one complete period Be sure to label te igest and lowest points on te grap 79 Find and state te amplitude and period lengt or te unction sin grap one complete period Be sure to label te igest and lowest points on te grap 6 and ten grap and ten
80 Find and state te amplitude and period lengt or te unction cos one complete period Be sure to label te igest and lowest points on te grap cos 4 8 Find and state te amplitude and period lengt o te unction one complete period Be sure to label te igest and lowest points on te grap sin 8 Find and state te amplitude and period lengt o te unction one complete period Be sure to label te igest and lowest points on te grap Trigonometric Identities: 8 and ten grap and ten grap and ten grap 8 Given tat 84 Given tat 85 Given tat 86 Given tat 87 Given tat cos and 0, ind te eact value o sin 4 6 0 tan and csc 0, ind te eact value o cos 9 4 7 csc and cos 0, ind te value o cos 5 sec and tan 0, ind te value o sin 4 tan and csc 0, ind te value o cos Inverse Trigonometric Functions: 88 Find te eact value o eac epression, it eists 8 (a) csc cos 4 89 Find te eact value o eac epression, it eists 4 cos cos (a) sinsin csc tan 4 90 Find te eact value o eac epression, it eists 7 5 (a) cos cos 4 sin sin5 9 Find te eact value o sec sin 6 5
9 Find te eact value o eac epression, it eists (a) sinsin 8 9 Find te eact value o tansin 7 94 Find te eact value o eac epression, it eists 4 cos cos (a) cos cos 6 5 95 Find te eact value o cot cos Solving Trigonometric Equations: tan tan 96 Find all primary solutions (ie 0 ) o te equation sec tan 97 Find all primary solutions (ie 0 cos 4 cos 98 Find all primary solutions (ie 99 Find all primary solutions (ie 0 00 Find all primary solutions (ie 0 Verying Trigonometric Identities: 0 Very tat te trigonometric equation is an identity sin ) o te equation 0 ) o te equation cos sin sin ) o te equation 9sin 9 4cos ) o te equation 4sin 7 8cos 4 4sincos 4sin cos 0 Very tat te trigonometric equation is an identity cos sin sin sin cos sin cos 0 Very tat te trigonometric equation is an identity cot sin sec csc 04 Very tat te trigonometric equation is an identity csc sin cos csc 05 Very tat te trigonometric equation is an identity tan sec cos sin
Solving non-linear Inequalities: 06 Solve te inequality 07 Let State your answer in interval notation 4 Find all numbers, any, suc tat 7 Please state your answer in interval notation 08 Let Find all numbers, any, suc tat answer in interval notation 6 6 6 Please state your 09 Let and g Find all numbers, any, suc tat g Average Rate o Cange Problems: t t 6t were time is 0 A ball is catapulted upwards Its eigt at time t is given by measured in seconds and eigt is measured in meters Wat is te average rate o cange o te eigt wit respect to time rom t to t? Find te average rate o cange o te unction log rom to 8 A painting as just been purcased At t years rom te date o purcase, te value o te 0 50t painting V in dollars is given by te unction 500 V t t Wat is te average rate o cange in te value o te painting during te time interval rom te 4 t year ater purcase to te 9 t year ater purcase? Please state your answer using proper units Trigonometric Applications: A sip is tied to two ancors on te soreline Te ancor line on te let orms a 46 angle wit te soreline and is 50 eet long Te ancor line on te rigt orms a 6 angle wit te soreline and is 8 eet long Find te eact distance (in eet) between te two ancors (A general picture is given below) Sip Ancor Soreline Ancor 4 Two wires stretc rom a pole to two points on te ground wic are 5 eet apart Te irst wire is to te let o te pole and orms a 0 angle wit te ground Te second wire is to te rigt o te pole and orms a 60 angle wit te ground How tall is te pole? Simply your answer 5 Greg watces as a ot air balloon rises and comes to a stop at a eigt o 7 eet Te angle o elevation o te ot air balloon rom were e is currently standing is 7 How ar does Greg need to walk e wants to stand directly underneat te balloon?