MATH 083 Final Exam Review

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1 MATH 08 Fial Eam Review Completig the problems i this review will greatly prepare you for the fial eam Calculator use is ot required, but you are permitted to use a calculator durig the fial eam period Calculators with advaced capabilities (such as the TI-89) or cell phoes are ot permitted The fial eam is cumulative ad cotais questios worth four poits each 1) Factor each polyomial completely y y y 7y 7 6y y 1 y 6y y 1 16m m 8m f) g) h) i) j) 1 8 y 0y 7t 1 1 m m m 1 ) Fid all umbers for which each ratioal epressio is udefied, if ay ) Simplify each ratioal epressio, if possible 7 8m 0m 1 16 ) Perform the idicated operatio ad simplify, if possible 917 a a a a a a a a a ) Solve t 1 t p p 1 p 1 p 1 y y y 7y m m f) y 16y 6 y y y 8 9y m m ) Determie whether each relatio is a fuctio Idetify the domai ad rage for each relatio,7,, 9,,10, 9,7, 0, 6 6, 7, 0,9, 1,, 6,1

2 7) Cosider the fuctios f ( ) ( f g)( ) ( f g)( ) ( f g)( ) f g 1 f ( ) 11 1 ; g( ) ; ad h ( ) Determie: f) ( f h)( ) g) ( g f)() h) ( g h)(1) f g i) 0 8) Does each graph represet y as a fuctio of? 9) State the domai of each fuctio 1 f( ) 10 g( ) h ( ) g ( ) f ( ) log 10) Use the give graph of f( ) o the followig page to aswer the eercises below Determie f ( 9) Determie f () For what value of is f( ) 6? For what value of is f( ) 9?

3 11) Use the graph of each fuctio to idetify its domai ad rage 1) Use radical otatio to rewrite each epressio Simplify, if possible 16 ab ) Simplify Assume that all variables i a radicad represet positive real umbers 16 6m y z a b c 9 1 m 1) Write the epressio usig a sigle radical

4 1) Add or subtract, as idicated Assume that all variables i a radicad represet positive real umbers y 80 8y y 1y ) Multiply ad simplify, if possible Assume that all variables i a radicad represet positive real umbers y y 10y 7 6 a b a b f) 1 g) 17) Simplify, if possible Assume that all variables i a radicad represet positive real umbers 10 6 ab 7 1 ab 9m ) Ratioalize each deomiator ) Solve 1 7 y ) Epress each umber i terms of i ad simplify, if possible ) Perform the idicated operatio Write the result i the form a bi ( 7 i) (1 i) f) (10 8 i) (6 9 i) 7 i(1 i) ( i)( i) 7 6i g) 6 i 1 i i

5 ) Solve each equatio by factorig 6 0 9m y 8 y( y ) ) Solve each equatio by usig the square root property r 77 y ) Solve each equatio by completig the square ) Solve each equatio by usig the quadratic formula 61 0 y y 1 6) Solve each equatio by the method of your choice ( )( 1) 90 0 p 6p 7) Fid the verte ad all - ad y-itercepts of the give fuctios Use this iformatio to sketch the graph of each fuctio The, idetify the domai ad rage of each fuctio f ( ) g ( ) 8) Sketch the graph of a quadratic fuctio with verte, 1 ad itercepts,0,,0, ad 0,8 9) Set up a table of coordiates for the fuctio Use the coordiates to sketch the graph of each fuctio The, idetify the domai ad rage of each fuctio f( ) 1 g ( ) h ( ) f( ) g( ) log 0) Write each equatio i its equivalet epoetial form log 16 1 log log1000 l e 1 1) Write each equatio i its equivalet logarithmic form a

6 ) Evaluate each epressio log7 ) Solve log8 8 f) log g) 1 log m 16 h) log7 1 ) A boat travels 60 miles per hour i still water Fid the speed of the river s curret if the boat traveled 80 miles dow the river i the same time that it took to travel 70 miles up the river ) Paul is preparig to complete quarterly ta reports for his employer Paul ca complete the reports i 1 hours if he works aloe His coworker Sharese ca complete the reports i 6 hours if she works aloe How log will it take to complete the reports if Paul ad Sharese work together? 6) A tire compay s reveue, R, i dollars is directly proportioal to the umber of tires,, it sells I a particular moth, the compay geerated reveue of $16,710 o the sale of, tires What is the compay s mothly reveue if,000 tires are sold? 7) The legth of a soud wave, w, i meters is iversely proportioal to the frequecy, f, of the soud i hertz (Hz) Bottleose dolphis emit clickig souds at differet frequecies for commuicatig, orietig themselves to their surroudigs, avoidig obstacles, ad fidig food If the wavelegth of a click that has a frequecy of 00 Hz is 1 meters, fid the wavelegth of a click that has a frequecy of 00 Hz 8) A stoe is throw upward with a iitial velocity of 8 feet per secod from a bridge 80 feet above a river The height of the stoe above the river t secods after it is throw is give by the fuctio s( t) 16t 8t 80 Whe does the stoe reach its maimum height? What is the maimum height? 9) The populatio of rabbits i a bar, P, after t weeks is modeled the fuctio Pt ( ) t the bar after 6 weeks? How may rabbit are i

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