( ) 1. 1) Let f( x ) = 10 5x. Find and simplify f( 2) and then state the domain of f(x).

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1 Mth 15 Fettermn/DeSmet Gustfson/Finl Em Review 1) Let f( ) = Find nd simplif f( ) nd then stte the domin of f(). ) Let f( ) = +. Find nd simplif f(1) nd then stte the domin of f(). ) Let f( ) = 8. Find nd simplif f( 5) nd then stte the domin of f(). ) Sketh the grph of the funtion g( ) = +, then stte the domin nd rnge of g(). 5) Sketh the grph of the funtion g( ) =, then stte the domin nd rnge of g(). 6) Sketh the grph of the funtion g( ) = + +, then stte the domin nd rnge of g(). 7) Simplif = ( + ) h() 6 (ssume tht the vribles n represent n rel number.) 8) Simplif h( ) = (ssume tht the vribles n represent n rel number.) 9) Simplif h( ) = 8 (ssume tht the vribles n represent n rel number.) 10) Simplif h( ) = (ssume tht the vribles n represent n rel number.) Simplif the following epressions using rtionl eponents nd the rules of eponents. ssume tht the vribles represent onl positive numbers nd epress our nswers in simplified et form using rtionl eponents where pproprite. 6 11) ( ) 7 1) ( ) 81 1) ( ) ) 1 15) m m 1 m ) ) ( ) 1 18) ( b ) 19) ( m ) n 0) ( ) 5 ( ) m n 8m n 1 1) ( 8 ) ( ) ) ( ) ( )

2 For the following epressions, use rtionl eponents to simplif nd then epress ou nswer in rdil form. ) 5b ) ) 8 0 q 6) ( ) Simplif the following rdil epressions. ssume tht the vribles represent onl positive numbers nd epress our nswers in simplified rdil form. 7) ) ) z 0) ) 9 ) ) 5 1 ) ) ) ) m n 1m n + m 75m n mn 7m n 8) Rtionlize eh denomintor. 5 9) ) 6 1) 1 ) ) ) Solve the following equtions for : 5) + = 6) = 7) = + 7 8) + 5 = 9) = 1 50) + 5 = Gustfson Finl Em Review

3 51) Solve r = 1 V for. 5) Solve d = 1V π for V 5) Solve r = 1 V for V 5) Solve = 5 + for b b Given the lengths of two sides of the right tringle, find the length of the missing side, rounded to two deiml ples. 55) =, b = 7 56) b = 11, = 1 57) = 5, = 7 b Find the distne between the given points. If the nswer is not et, use lultor nd give n pproimtion to the nerest tenth. 58) (7, 5) nd (, ) 59) (, 9) nd (, 6) 60) (, 7) nd (, 5) 61) (5, 8) nd ( 5, ) Simplif eh of the following epressions. Epress our nswer in + bi form. 6) ( 1 + i ) ( 6 6i ) 6) ( 10 i ) ( 6i ) i i 65) ( 81)( ) 6) ( 8 1 ) ( 7 ) 66) ( )( 5 ) 67) ( 6 5 )( 9 ) 7 68) 6 i 5 69) 1 i 70) i 71) 5 + 8i i 7) 7 i 5 + i 7) 5 + i + 6i 7) 76) 7 i 75) 17 i 77) 0 i 0 i Gustfson Finl Em Review

4 Solve for using the method of our hoie. Epress irrtionl nswers in simplified rdil form nd omple nswers in + bi form: 78) ( 1) 1 = 0 79) ( ) 8 = 0 80) ( 10) 8 = 0 81) + 0 = 1 8) 1 = 8) = 1 omplete the squre on the following polnomils nd then ftor the resulting perfet-squre trinomil. 8) 8 + = ( ) 85) = ( ) 86) + = ( ) 87) = ( ) Solve the following qudrti-like qudrti equtions for using u substitution. 88) + 0 = 9 89) 51 = ) 1 = 1 91) ( + ) + 5( + ) = 1 Solve the following literl (like formul) eqution for. 9) m = np k 9) = b 9) r = st u Given the following qudrti funtions, for eh problem: ) find the verte. b) find the -interepts, epress s ordered pirs, nd if the re irrtionl, round to the nerest tenth. ) determine if the verte is mimum or minimum. d) find the eqution of the is of smmetr. e) find the -interept nd epress s n ordered pir. f) using ll the informtion gthered from bove, sketh the prbol. 95) f() = ) f() = + 97) f() = ) f() = 5 Solve the following qudrti inequlities, stte our nswer in intervl nottion, nd grph our nswer on number line. 99) 100) 101) ) 8 + > 10 Gustfson Finl Em Review

5 10) You hve 5 feet of fening to enlose retngulr region. Find the dimensions of the retngle tht mimize the enlosed re. Wht is the mimum re? 10) The profit tht vendor mkes per d b selling pretzels is given b the funtion P() = Find the number of pretzels tht must be sold to mimize the profit. Wht is the mimum profit? 105) You hve 7 feet of fening to enlose three sides of retngulr region. Find the dimensions of the retngle tht mimize the enlosed re. Wht is the mimum re? 106) mong ll pirs of numbers whose sum is, using lgebr, find pir whose produt is s lrge s possible. 107) person stnding lose to the edge on top of n 88-foot building throws bsebll vertill upwrd. The qudrti funtion s(t) = 16t + 6t + 88 models the bll s height bove the ground, s(t), in feet, t seonds fter it ws thrown. How mn seonds does it tke until the bll finll hits the ground? Round to the nerest tenth of seond if neessr. 108) Repet #107 if the person is on top of 105-foot building nd the funtion is s(t) = 16t + 6t ) Repet #107 if the person is on top of 08-foot building nd the funtion is s(t) = 16t + 6t Given the following pirs of funtions, for eh pir find the following: ) (f g)() b) (fg)() ) (f g)() d) (g f)() g e) the domin of ( ) f 110) f() = + nd g() = 1 111) f() = 1 nd g() = + 11) f() = nd g() = For the given funtions: ) find the formul for the inverse funtion nd epress our nswer using f 1 (). b) grph f() nd f 1 () on the sme grid. 11) f() = ) f() = ) f() = 1 Gustfson Finl Em Review 5

6 Given the following grphs of f(), nswer the following questions: ) Is it the grph of 1 1 funtion? Wh? b) Does it hve n inverse funtion? ) Evlute f( ), f 1 (0), f(f()), f 1 (f(1)) 116) 117) 118) Grph the following funtions nd nswer the following questions bout eh grph. ) Wht is the domin of the funtion? b) Wht is the rnge of the funtion? ) Is the funtion inresing or deresing? d) Wht is the eqution of the smptote? 119) f() = ( 1) 10) f() = ) f() = ( + ) 1) f() = log ( ) 1) f() = log 1) f() = log +. 15) The grph of f() = will pss through the points (0, m) nd (n, 16). Find m nd n. 16) The grph of f() = will pss through the points (1, m) nd (n, 9). Find m nd n. 17) The grph of f() = 5 will pss through the points (, m) nd (n, 15). Find m nd n. 18) The grph of g() = log will pss through the points (8, p) nd (r, ). Find p nd r. 19) The grph of g() = log will pss through the points (6, p) nd (r, 0). Find p nd r. 10) The grph of g() = log 5 will pss through the points (5, p) nd (r, 1). Find p nd r. Gustfson Finl Em Review 6

7 onvert between eponentil form nd logrithmi form to solve for in eh problem below. 11) log 16 = 1) ln e 5 = 1) log 7 = 1) log 51 = 15) log 0.1 = 1 16) log 9 = 17) log 6 = 18) log 16 = ) log 5 5 = 10) log = 5 11) irle ll of the sttements below whih re true for ll positive rel numbers nd. ) log( ) d) log ( ) = log log b) log(m P ) = P log M ) ln ln = e) e (ln ) = f) log( e ) g) log( ) + log( ) = log( ) h) log ( + ) = (log )(log ) i) ln( ) j) log = k) log = log log log = log log l) log = = = ln ln Find the vlues of the following logrithms. DO NOT use our lultor nd show our work. 1) ln e 1) ln e 1) ln 1 15) log ) log 17) log ) log ) log ) log ) log ) log 81 15) log ) log ) log ) log ) log ) log 159) ln 5 e Gustfson Finl Em Review 7

8 Epnd the epressions below so tht the re epressed in terms of the logrithms of,, nd z. 160) logb 161) z log z 5 b 16) 6 log 16) z b log z b 9 ondense the epressions below so tht the re written s logrithm of one quntit. 16) log5 log5 166) log( ) 9log 1 log log b b 165) ( + ) ( ) 167) log5 + 1 log5 log5 z Given tht the log = 0.69, log b = 1.099, nd log = nd using the properties of logrithms, find the vlue of eh epression below. 168) log b 169) log 9 170) log b 171) log b 17) 6 b log 17) log b Find the following to four deiml ples. 17) log ) log ) log ) log 0. 0 Solve eh eqution for. Epress our nswer in et form nd then, if it is irrtionl, round to four deiml ples. 178) ( 1) = 9 179) 5 = ) 7 = ( ) 181) ( + 6) = 18) + 6e = 5 18) e = 16 18) 5e = 8 185) 6 + 5e = 1 186) 6 + 5ln ( + ) = 187) 6ln (9) = 1 188) ln ( + 6) = 189) ln ( 1) = 190) log ( ) log = 191) log 6 + log 6 ( 1) = 1 19) log ( ) + log ( + ) = 19) log + log ( + 6) = Gustfson Finl Em Review 8

9 For eh problem below: ) find P 0 or 0 b) find k nd round our nswer to 5 deiml ples. ) use our nswers to () nd (b) bove to stte the model funtion, either P = P 0 e kt or = 0 e rt d) use our model from () bove to estimte the P or fter the given vlue for time, t e) use our model from () bove to estimte when the vlue of P or will reh the given vlue. 19) The hlf-life of silion- is 710 ers. If 0 grms is present now, how muh will be present in 900 ers? (Round our nswer to three deiml ples) When will the mount be 15 grms? 195) The hlf-life of rdium is 1690 ers. If 0 grms re present now, how mn grms will be present in 100 ers? When will the mount be 15 grms? 196) roh popultion of 500, if left untreted, will grow to 50 in 1 d. Estimte the popultion fter 10 ds. fter how mn ds will the roh popultion double to 1000? 197) n endngered speies of fish hs popultion tht is deresing eponentill. The popultion 8 ers go ws Tod, onl 1100 of the fish re live. Wht will the popultion be in ers? When will the popultion drop below 100? 198) The popultion of prtiulr ountr ws 8 million in In 00 it ws 8 million. Wht ws the popultion in 005? When will the popultion be 60 million? 199) teri is lbortor ulture inresed from n initil popultion of 00 to 1000 in 0 minutes. Estimte the popultion in 1 hour. Estimte when the popultion will reh 1 million. Identif the equtions below using one of the following: ) irle ) n ellipse ) horizontl prbol opening left D) vertil prbol opening down E) horizontl prbol opening right F) vertil prbol opening up G) hperbol opening up nd down H) hperbol opening left nd right 00) = 0 01) = 6 0) + 6 = 0) = 0 0) = 16 05) 8 = 06) = ) = 6 08) + = ) + 9 = 8 10) + 5 = 11) = 6 Gustfson Finl Em Review 9

10 Write eh of the following in stndrd form nd grph it. Nme the enter s n ordered pir. 1) = 0 1) = 0 1) = 6 15) = 0 Write the following in stndrd form nd grph it. Nme the enter nd verties s ordered pirs nd give the equtions of n smptotes. 16) ( 1) ( + ) = 17) 16( 1) 9( ) = 1 18) 5( + ) 9( + 1) = 5 19) ( + ) 5( ) = 100 Grph the following equtions. Nme the verte, -interept, nd -interepts, s ordered pirs. 0) + = 1) = 0 ) = + 5 ) = Grph the following equtions. ) = 1 5) = 8 6) = 10 7) = Write the generl form eqution of the irle with the given rdius nd enter. 8) rdius = 5, enter = (, ) 9) rdius =, enter = (, 5) 0) rdius = 7, enter = (, 6) 1) rdius =, enter = ( 5, ) Solve the following sstems of equtions using the method of our hoie. ) = 6 ) + = + = 17 = ) + = 1 5) + = 16 = 1 + = 6) = 5 7) 5 + = = = 100 8) + = 9) ( ) + ( + 5) = 0 = 1 + = 9 Gustfson Finl Em Review 10

11 Given the line segment, interseting the given hperbol, find the length of the line segment, or. Epress our nswer in et form, nd then pproimte our nswer to deiml ples. Find the oordintes of the point. 0) = 1 1) 5 5 = (, 0 ) (, 0) ) = 1 ) 5 7 = 8 1 (0, ) (0, ) ) The digonl of grden is 119 feet. The re of the grden is 5880 squre feet. Find the length nd the width of the grden. 5) The re of grden is 780 squre feet nd the length of its digonl is 111 feet. Find the dimensions of the grden. 6) The re of retngle is squre meters. The length of the digonl is meters. Find the dimensions of the retngle. 7) Dtport Eletronis needs retngulr memor bord tht hs perimeter of 8 entimeters nd digonl of length 10 entimeters. Wht should the dimensions of the bord be? 8) The New World tile ompn wnts to mke new retngulr tile tht hs perimeter of 6 inhes nd digonl of length 5 inhes. Wht should the dimensions of the tile be? 9) The rgo re of deliver vn must be 60 squre feet, nd the length of digonl must ommodte 1 foot bord. Find the dimensions of the rgo re. Gustfson Finl Em Review 11