1. Find the distnce between the pir of points. Give n ect, simplest form nswer nd deciml pproimtion to three plces., nd, MAC 110 Finl Em Review, nd,0. The points (, -) nd (, ) re endpoints of the dimeter of circle. Find the length of the dimeter. Find the length of the rdius. Find the center of the circle. d. Write the eqution of the circle. e. Sketch the grph of the circle. 6. Stte the intervls on which the function is ) incresing, b) decresing, nd c) constnt.. Given tht f ( ) nd g( ) 1, find f(-) g( + h) (f + g)() d. (f - g)() e. (f g)() f. ( g f )( ) g. f g f ( h) f( ) h. h. Find the domin of ech function. Write your nswers in intervl form. f( ) f( ) 1 h ( ) d. g ( ) e. g ( ). Grph the function f( ) 1 (round your nswers to three deciml plces) stte the reltive mimum nd/or minimum stte intervls over which the function is incresing nd decresing stte nd y intercepts d. find f() 8. Given rectngle whose length, L, is twice its width, w: ) Epress the re s function of w b) Epress the perimeter s function of w c) Epress the digonl s function of w. 9. A crpet instller uses ft of linen tpe to bind the edges of rectngulr hll runner. If the runner is feet wide, epress its re s function of the width.. Write slope-intercept eqution for line with the given chrcteristics. Psses through (, 0) nd (-1, ) Slope is undefined nd the line psses 1 through, Psses through (, -) nd is prllel to y d. Psses through (, -) nd is perpendiculr to y 1
10. Given the function shown, use trnsformtions to grph the following function stted. (lbel pts on your grphs) y f( ) 1. Write in + bi form. i i i i ( 1 i) 16. Solve by using the qudrtic formul 1 0 1. Solve by the completing the squre method. 1 0 Grph: ) y = f( - ) d) y = f() + b) y = f( - ) e) y = - f() c) y f 1 ( ) f) y = - f() 11. Solve: () ( ) 1. A privte plne leves Orlon Airport nd flies due est t speed of 180 km/h. Two hours lter jet leve Orlon Airport nd flies due est t speed of 900 km/h. How fr from the irport will the jet overtke the privte plne? 1. A trin leves Little Rock, Arknss, nd trvels north t 8 kilometers per hour. Another trin leves t the sme time nd trvels south t 9 kilometers per hour. How long will it tke before they re 1 kilometers prt? 1. Jeff leves his house on his bicycle t 8:0 A.M. nd verges miles per hour. His wife, Jon, leves t 9:00 A.M., following the sme pth nd verging 8 miles per hour. At wht time will Jon ctch up with Jeff? 18. Find the zero(s) of ech function. f ( ) f ( ) 19. Write the function y 8 in the form y ( h) k. Stte the verte, the ect vlues of the nd y intercepts, nd the domin nd rnge. Grph the qudrtic function. 0. A projectile is thrown upwrd so tht its distnce in feet bove the ground fter t seconds is ht ( ) 16t 8t 0. After how mny seconds does it rech its mimum height? Wht is the mimum height it reches? 1. Solve:. Solve: 1 1. 6 1. Solve:. Solve: 1. Solve: 1 6. Solve:
. Solve for : y w 8. Solve for m: 1 1 1 F m p 9. Solve nd write intervl nottion for the solution set. 6 6 0. Given tht y vries directly s nd inversely s the squre of w, find the constnt of vrition, k, if y= when = nd w=. 1. Stte the symptotes for the following functions: y y y 1. Epress in terms of sums, differences, nd/or multiples of rithms: b 8b 6. Describe how to use trnsformtions to obtin the grph of y from the grph of the bsic eponentil function. Stte the symptote nd the y-intercept.. Sketch the grph of the following rithmic function: f( ) ( ) 8. Epress s single rithm nd simplify. 1 1 1 y y 16 ln [ln( 9) ln( )]. Grph the rtionl function: 1 f( ) Stte the domin, V.A., H. A., -int, y-int, then sketch the grph.. f f. 1 1 Given ( ), find ( ).. Suppose the mount of rdioctive element remining in smple of 100 milligrms fter yers cn be described 0.01906 by A ( ) 100e. How much is remining fter 0 yers? Round the nswer to the nerest hundredth of milligrm. 9. Find ech of the following. 10 t ln e 8 b b d. 1 0. Given tht 0.01, 0.8, nd 11 1.01 Find ech of the following. 98 11 11
1. Solve. Give the EXACT solution(s) nd, where pproprite, deciml pproimtion to three plces. 8 1 e d. ( 1) e. ( ) 1 ( ) ( ) () f.. Solve. Tickets for the school ply cost $ for students nd $8 for dults. On opening night, ll 60 sets were filled, nd the bo office revenues were $80. How mny student nd how mny dult tickets were sold? 6. Find the center nd the length of the rdius of the circle, ( ) ( y1) 16, nd grph it. g. ln( ). Solve lgebriclly. y 8 y 1 1 8y 1 y 6. Grph the piecewise function.. Solve. 0 1, 0 Center Rdius Jim wnts to pln mel with 18 grms of crbohydrtes nd 980 clories. If green bens hve grms of crbohydrtes nd 0 clories per hlf cup serving nd if French fried shrimp hve 9 grms of crbohydrtes nd 190 clories per three-ounce serving, how mny servings of green bens nd shrimp should he use?
MAC110 Finl Em REVIEW ANSWER KEY: 1. ) d 89 d 9. b) d 10 1 d.1. ) dimeter length: b) rdius length: c) center: 9 1, 9 1 d) Eqution: y e) 1. ) y 1 b) c) y 1 9 d) y 6. ) inc,,(,) b) dec (1, ) c) constnt (,1). ) m: 16. min: -1. b) inc, 1.8,(1.8, ) dec 1.8,1.8 c) -int: (.1,0),(.1,0),(.1,0) y-int: (0, ) d) f () 18 8. ) Aw ( ) w b) Pw ( ) 6w c) dw ( ) w. ) f( ) b) g h h h h c) ( f g)( ) d) e) f) ( g f)( ) 110 9 g) ( f g)( ) 116 f ( h) f( ) h) = 10 + h h. ) (, ) b) (,) (, ) ( ) 6 1 ( f g)( ) 8 ( fg)( ) 1 10 1 8 d) (,] e) (, ) c),,1 1, 9. A ( ) 6 10. Below is the list of ordered pirs you should obtin fter the trnsformtion(s) is done for ech given function. ) (0, 0), (, 1), (, ) b) (, 0), (0, 1), (-1, ) c) (0,-), (1, 0), (, 1) d) (-, ), (0, ), (1, ) e) (-, 0), (0, -1), (1, -) f) (-, -), (0, -), (1, -6) 1 11. 1. 0 km
1. 1 hours 1. 9:0 m 1. ) 19 i b) 16. 1. 18. ) 1 i 1 i 1 b) 1 i c) i 19. To write in the requested form: y 8 y ( h) k y ( ) y ( ) () y( ) Verte: (, -) -int: 10,0 y-int: (0, ) domin:, rnge: [, ). {-, }. No solution. {1} 1. 6.. 8. 1, y w m Fp p F 11 1 9. ), b) (, ] [ 1, ) 0. k = 18 1. ) y b) y 0, c) y, 1 1, (, ). domin: VA: 1, H.A.: y -int:,0 1 y-int: 0, 0. time: 1.1 sec m height: 0. ft 1. {8} 6
. f 1 ( )..09 mg. ( ) () b b 6. trnsformtions: right units, up units symptote: y = y-int: 0,. e g).19. ) {(-, 1)} b) No solution.. 0 hlf cups of bens nd three-ounce servings of shrimp. 100 student tickets nd 60 dult tickets 8. ) y 11 6 6. b) ln ( ) 9. ) t b) c) d) - 0. ) 1.886 b) 0.9 c) 0.89 1. ) = -1 b) () 0. c) ln().61 d) = 10 e) No solution f) = Center (-,1) rdius = units