ࡱ>  {~I_ Dbjbj bbmJJJ^^^^^Fv6{<{<{<AFCFCFCFCFCFCF$8HJzgFJ{<7{<{<{<gFC|FmBmBmB{<hJAFmB{<AFmBmB:"EcvE8<:E -FF0FE.dK<dKEE0dKJE@{<{<mB{<{<{<{<{<gFgF@{<{<{<F{<{<{<{<dK{<{<{<{<{<{<{<{<{< : Name ___________________________ AP Calculus AB 2015 Summer Assignment Dear AP Calc Student, Welcome to AP Calculus! I am looking forward to working with you this coming September. This is your first assignment the summer review packet. It is a review from Chapter 1. Neatly show the work and solution for each problem assigned using pencil. Please do not use pen. Correct work must be shown for full credit. Review the families of functions, in your function notebook, as part of this packet. You will have a quiz on this material within the first week of school. You should also know your unit circle. Please make sure that your function notebook is up to date. You can check my Teacher Page on School Wires for this information. You should have the material from Chapter 1 and the first part of Chapter 2. There will be a Function Notebook check when we complete Chapter 2. A graphing calculator that you can operate is required for this class. I will be using the TI 84 and TInspire. It is expected that you have a moderate proficiency skill level with your calculator. Our goal is to be ready for the AP Test scheduled for early May. You will practice open ended questions and take practice tests to prepare your for this test. Also, I hope that you plan on competing in Math League, which will be held on Tuesdays after school. If you have any questions, please contact Mrs. Brumberg email:  HYPERLINK "mailto:mbrumberg@wtps.org" mbrumberg@wtps.org or  HYPERLINK "mailto:mbrumberg74@gmail.com" mbrumberg74@gmail.com. I do check my school email from home. See you in September. Mrs. Brumberg Parametric Equations      SHAPE \* MERGEFORMAT  Circles  Examples of Circles  Square both equations and add them together.  SHAPE \* MERGEFORMAT  Ellipses  Lines, line segments and many other curves can be defined parametrically.   SHAPE \* MERGEFORMAT  Parametrization for a line Use the formulas  EMBED Equation.DSMT4  Assign t = 0 to your first point. Assign t = 1 to your second point (This choice is for convenience. Making it more complicated is okay too but unnecessary) Lets go through the steps to finding a parametrization for a line segment containing (-2, 1) and (3, 5) 1. Let t = 0, x = -2, and y = 1 and find  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  2. Now use t = 1, x = 3, and y = 5 to find a and b  EMBED Equation.DSMT4   EMBED Equation.DSMT4  3. Write the answer  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  This is just one possible answer. Try these! Find a parametrization for a line segment containing the points. a) (1,3) and (2,5) b) (-2, 6) and (4,2) Summer Assignment AP Calculus Name ______________            Quick Check Chapter 1      x- 224f(x)421Assessment Chapter 1   SHAPE \* MERGEFORMAT    EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  In applications, t often denotes time, an angle or the distance a particle has traveled along its path from a starting point. Parametric graphing can be used to simulate the motion of a particle.  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If is a closed ints~~~~C?@ Trebuchet MS@wIw @wfg-"2 erval, , the point~-G@ Trebuchet MS@wIw @wfg-C2 (, is the initial point of the curve and ~~~~~-%@ Trebuchet MS@wIw @wfg-2 the point ,~+ 2@ Trebuchet MS@wIw @wfg-2 is the te~ @ Trebuchet MS@wIw @wfg- 2 tI$CZ@ Trebuchet MS@wIw @wfg- 2 Iatb-@ Trebuchet MS@wIw @wfg-2 fagafbgb'C$@Euclid Symbol@wIw @wfg- 2 ]+ @ Trebuchet MS@wIw @wfg-C2 (rminal point of the curve. When we gives~~P~+ &@ Trebuchet MS@wIw @wfg-(2  parametric equations s~~ +@ Trebuchet MS@wIw @wfg-C2 (and a parameter interval for a curve, wes~P a @ Trebuchet MS@wIw @wfg-62  say that we have parametrized Ps~k2@ Trebuchet MS@wIw @wfg-C2 (the curve. A grapher can draw a paramet PskA!@ Trebuchet MS@wIw @wfg-02 rized curve only over a clo~k6@ Trebuchet MS@wIw @wfg- 2 sed  2@ Trebuchet MS@wIw @wfg-C2 (interval, so the portion it draws has en~~~P @ Trebuchet MS@wIw @wfg-:2 "dpoints even when the curve being ~P~+@ Trebuchet MS@wIw @wfg-!2 graphed does not.t&W AppsMFCC0 0 Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  The variable t is a parameter for the curve and its domain I is the parameter interval.  If I is a closed interval, ad"td"b, the pointfa(),ga()() is the initial point of the curve and the point fb(),gb()()is the terminal point of the curve.  When we give parametric equations and a parameter interval for a curve, we say that we have parametrized the curve.  A grapher can draw a parametrized curve only over a closed interval, so the portion it draws has endpoints even when the curve being graphed does not. & N"Systemgfg !-NANIuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  The variable t is a parameter for the curve and its domain I is the parameter interval.  If I is a closed interval, ad"td"b, the pointfa(),ga()() is the initial point of the curve and the point fb(),gb()()is the terminal point of the curve.  When we give parametric equations and a parameter interval for a curve, we say that we have parametrized the curve.  A grapher can draw a parametrized curve only over a closed interval, so the portion it draws has endpoints even when the curve being graphed does not. FMathType 6.0 Equation MathType EFEquation.DSMT49qOle CompObjHKiObjInfoOlePres000JL@': ?.  4&4[ & MathType` m3 Trebuchet MS@wIw @w fi- 2 2y@ Trebuchet MS@wIw @w fi-C2 (Describe the graph of the relation deter~~@ Trebuchet MS@wIw @w fi-2 mined by ,1.s~'@ Trebuchet MS@wIw @w fi- 2 xtyt )@Euclid Symbol@wIw @w fi- 2 ==-9`?&sAppsMFCCLLDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Describe the graph of the relation determined by  x==t,y==1"-t 2 . & N"Systemi fi !-NANILTPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Describe the graph of the relation deterEquation Native h_1306136219AYOFkkOle CompObjNQimined by  x==t,y==1"-t 2 . FMathType 6.0 Equation MathType EFEquation.DSMT49qy-  zObjInfoOlePres000PRLEquation Native _1306136550UFkk.   @)&) & MathType B Trebuchet MS@wIw @w fA- 2 2y\ Trebuchet MS@wIw @w fA- 2 11+@ Trebuchet MS@wIw @w fA-=2 $Set ,1, and use the parametric mode N s~s2@ Trebuchet MS@wIw @w fA-92 !of the grapher to draw the graph.P-@ Trebuchet MS@wIw @w fA- 2 xtyt@Euclid Symbol@wIw @w fA- 2 ==-`z&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Set x 1 ==t,y 1 ==1"-t 2 , and use the parametric mode of the grapher to draw the graph. & N"SystemA fA !-NANIPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_H  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEGHIJKLMNOPQRSTUVWXYZ[\]`cdefghijklmnopqrstuvwxyz{|A@AHA*_D_E_E_A  Set x 1 ==t,y 1 ==1"-t 2 , and use the parametric mode of the grapher to draw the graph. FMathType 6.0 Equation MathType EFEquation.DSMT49q%B  .   <&; & MathType Ole  CompObjTW iObjInfo OlePres000VX "@ Trebuchet MS@wIw @wf-C2 (Describe the graph of the relation deter~~@ Trebuchet MS@wIw @wf-2 mined by s~@@ Trebuchet MS@wIw @wf-2 3cos,3sin,02.$V$~@ Trebuchet MS@wIw @wf-C2 (Find the initial points, if any, and ind~~~~~~~@ Trebuchet MS@wIw @wf-B2 'icate the direction in which the curve d~~~~P~ 2@ Trebuchet MS@wIw @wf-2 is traced. 2~ @ Trebuchet MS@wIw @wf-@2 &Find a Cartesian equation for a curve ~ ~~@@@ Trebuchet MS@wIw @wf-2 xtytt?-@@Euclid Symbol@wIw @wf- 2 py@r@Euclid Symbol@wIw @wf- 2 ==y @ Trebuchet MS@wIw @wf-?2 %that contains the parametrized curve.~s~&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Describe the graph of the relation determined by x==3cost,y==3sint,0d"td"2p.Find the initial points, if any, and indicate the direction in which the curve is traced. Find a Cartesian equation for a curve that contains the parametrized curve. & N"Systemf !-NANIPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEEquation Native F_1306136614S_[Fk/Ole ^CompObjZ]_iuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Describe the graph of the relation determined by x==3cost,y==3sint,0d"td"2p.Find the initial points, if any, and indicate the direction in which the curve is traced. Find a Cartesian equation for a curve that contains the parametrized curve. FMathType 6.0 Equation MathType EFEquation.DSMT49q‘PRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x 2 ++y 2 ==9cos 2 t++ObjInfoaOlePres000\^[Equation Native b_1306136802aF//E( H a.   `?& ?s & MathType @dEuclid Symbol@wIw @wf- 2 (y@O"dEuclid Symbol@wIw @wf- 2 )y*%Euclid Symbol@wIw @wf- 2 (y*&Euclid Symbol@wIw @wf- 2 )y> Trebuchet MS@wIw @wf- 2 2yBI Trebuchet MS@wIw @wf-2 22222~ hw Trebuchet MS@wIw @wf- 2 22 @ Trebuchet MS@wIw @wf-"2 9cos9sin9cossin919$($~X~7@@@ Trebuchet MS@wIw @wf-2 Thus, 9@@ Trebuchet MS@wIw @wf-C2 (This represents the equation of a circle~~~;@ Trebuchet MS@wIw @wf-C2 ( with radius 3 and center at the origin.P~~~~=@ Trebuchet MS@wIw @wf- 2   @@ Trebuchet MS@wIw @wf-C2 (As increases from 0 to 2 the curve is ^~s ~ E @ Trebuchet MS@wIw @wf--2 traced in a counter-clock,~ @@ Trebuchet MS@wIw @wf-2 xytttth@@ Trebuchet MS@wIw @wf- 2 xy @ Trebuchet MS@wIw @wf- 2 ty n@Euclid Symbol@wIw @wf- 2 py M@Euclid Symbol@wIw @wf-2 +=+=+==z':@ 2 += 4@ Trebuchet MS@wIw @wf-2 wise directionP~~~ $@ Trebuchet MS@wIw @wf-32 beginning at the point (3,0).~~~a&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x 2 ++y 2 ==9cos 2 t++9sin 2 t==9cos 2 t++sin 2 t()==91()==9Thus,  x 2 ++y 2 ==9This represents the equation of a circle with radius 3 and center at the origin.  As t increases from 0 to 2p  the curve is traced in a counter-clockwise directionbeginning at the point (3,0). & N"Systemf !-NANI9sin 2 t==9cos 2 t++sin 2 t()==91()==9Thus,  x 2 ++y 2 ==9This represents the equation of a circle with radius 3 and center at the origin.  As t increases from 0 to 2p  the curve is traced in a counter-clockwise directionbeginning at the point (3,0). FMathType 6.0 Equation MathType EFEquation.DSMT49qOle }CompObj`c~iObjInfoOlePres000bdkTPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Parametrizations of ellipses are similaI> _ .   8&@8 & MathType-@0 | | | "| $ ?l Trebuchet MS@wIw @wf- 2 22b Trebuchet MS@wIw @wf- 2 22 6  Trebuchet MS@wIw @wf- 2 22 ,  Trebuchet MS@wIw @wf- 2 22@ Trebuchet MS@wIw @wf-C2 (Parametrizations of ellipses are similars~~~~s~@ Trebuchet MS@wIw @wf-:2 " to parametrizations of circles. s~~~9@ Trebuchet MS@wIw @wf-C2 (Recall that the standard form of an ellis9@ Trebuchet MS@wIw @wf--2 pse centered at (0, 0) is~ @ Trebuchet MS@wIw @wf- 2 1. @ Trebuchet MS@wIw @wf--2 For cosand sin,we have 1~7Pgq@@ Trebuchet MS@wIw @wf-2 which P~c@ Trebuchet MS@wIw @wf- 2 xy| `@ Trebuchet MS@wIw @wf- 2 ab -@ Trebuchet MS@wIw @wf- 2 xy -@ Trebuchet MS@wIw @wf-2 xatyat|H*@ Trebuchet MS@wIw @wf- 2 ab {@Euclid Symbol@wIw @wf- 2 += _ 2 ==+=U q]@ Trebuchet MS@wIw @wf-C2 (is the equation of an ellipse with cente~~~P~q.$@ Trebuchet MS@wIw @wf-2 r at the origin.~~&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Parametrizations of ellipses are similar to parametrizations of circles.  Recall that the standard form of an ellipse centered at (0, 0) is x 2 a 2 ++ y 2 b 2 ==1.For x==acostand  y==asint,we have  x 2 a 2 ++ y 2 b 2 ==1which is the equation of an ellipse with center at the origin. & N-"Systemf !-NANIEquation Native _1306136896'gF/POle CompObjfiir to parametrizations of circles.  Recall that the standard form of an ellipse centered at (0, 0) is x 2 a 2 ++ y 2 b 2 ==1.For x==acostand  y==asint,we have  x 2 a 2 ++ y 2 b 2 ==1which is the equation of an ellipse with center at the origin. FMathType 6.0 Equation MathType EFEquation.DSMT49qTPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  If the parametrization of ObjInfoOlePres000hj|Equation Native p_1306212746qmFPP:*+K) h .   D&`D & MathTypeP @ Trebuchet MS@wIw @wvf-$2  ,2,02 . H hH7@ Trebuchet MS@wIw @wvf-%2  min int Hq8s~~H2H@ Trebuchet MS@wIw @wvf-2 . !2@ Trebuchet MS@wIw @wvf-C2 (Iftheparametrizationofacurveisxtyttgraph~zsz^gZ6@ Trebuchet MS@wIw @wvf-2 thecurve72@ Trebuchet MS@wIw @wvf-C2 (Findtheinitialandteralposandindicatethed-$-^7r-@ Trebuchet MS@wIw @wvf-*2 irectioninwhichthecurvewP@ Trebuchet MS@wIw @wvf-=2 $istracedFindaCartesianequationforacu^ l@Euclid Symbol@wIw @wvf-2 ==+&@ Trebuchet MS@wIw @wvf-2  8Hn w h@ Trebuchet MS@wIw @wvf-2 . ?mhHHn " $@ Trebuchet MS@wIw @wvf-42 rvethatcontainstheparametrized^^sw +@ Trebuchet MS@wIw @wvf-C2 (curveWhatportionoftheCartesianequationis^z w (@ Trebuchet MS@wIw @wvf-12 tracedbytheparametrizedcurves&{AppsMFCCTTDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  If the parametrization of a curve is x==t,y==t++2,0d"td"2 graph the curve.   Find the initial and terminal points and indicate the direction in which the curve is traced. Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the Cartesian equation is traced by the parametrized curve? & N"Systemvf !-NANIa curve is x==t,y==t++2,0d"td"2 graph the curve.   Find the initial and terminal points and indicate the direction in which the curve is traced. Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the Cartesian equation is traced by the parametrized curve?Ole CompObjloiObjInfoOlePres000np, FMathType 6.0 Equation MathType EFEquation.DSMT49qH  .   A&As & MathTypeP )Euclid Symbol@wIw @wf- 2 (y--Euclid Symbol@wIw @wf- 2 )y Euclid Symbol@wIw @wf- 2 (y Euclid Symbol@wIw @wf- 2 )y Euclid Symbol@wIw @wf- 2 (y $Euclid Symbol@wIw @wf- 2 )y@ Trebuchet MS@wIw @wf-<2 #If and 2, then by substitution 2.F~E~~]@@ Trebuchet MS@wIw @wf-C2 (The graph of the Cartesian equation is a ~~~@ Trebuchet MS@wIw @wf-+2  line through0,2with 1.~.P~ @@ Trebuchet MS@wIw @wf-C2 (The segment of that line from 0,2 to 2s~sll ;"@ Trebuchet MS@wIw @wf-@2 &,4is traced by the parametrized curve.~s~@ Trebuchet MS@wIw @wf-2 xtytyx2@ Trebuchet MS@wIw @wf- 2 my@Euclid Symbol@wIw @wf-2 ==+=+4 2 =y&LAppsMFCC%%Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  If x==t and y==t++2, then by substitution  y==x++2.The graph of the Cartesian equation is a line through0,2()with  m==1.The segment of that line from 0,2()  to  2,4()is traced by the parametrized curve. & N"Systemf !-NANI%lPR<DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HEquation Native A_1306137019wsFPPOle CompObjrui      !"#$%&'()*+,-/01234567:=>?@ABCDEFGHIJKLNOPQRSVYZ[\]^_`abcdefghijklmnopqrsvyz{|}~A@AHA*_D_E_E_A  If x==t and y==t++2, then by substitution  y==x++2.The graph of the Cartesian equation is a line through0,2()with  m==1.The segment of that line from 0,2()  to  2,4()is traced by the parametrized curve. FMathType 6.0 Equation MathType EFEquation.DSMT49q!_v GObjInfoOlePres000tvEquation Native .x_1306137005yF`܄.  &@ & MathType @ Trebuchet MS@wIw @wfU-C2 (Initial point (0,2) Terminal point (2,4~~~~ws~~w@ Trebuchet MS@wIw @wfU- 2 )y7+@ Trebuchet MS@wIw @wfU-:2 "Curve is traced from left to right ~s~G&AppsMFCC\\Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  Initial point (0,2)  Terminal point (2,4)Curve is traced from left to right & N"SystemUfU !-NANI\PRDSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  Initial point (0,2)  Terminal point (2,4)Curve is traced from left to rightOle 8CompObjx{9iObjInfo;OlePres000z|<" FMathType 6.0 Equation MathType EFEquation.DSMT49q .  `&, & MathType` @ Trebuchet MS@wIw @wf -2 ,2,02@@ Trebuchet MS@wIw @wf -2 xtytt?r@Euclid Symbol@wIw @wf -2 ==+y\&AppsMFCCyyDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x==t,y==t++2,0d"td"2 & N"System f !-NANIyPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolCourier NewTimes New RomanEuclid Extra!OED/APG_APAPAE%B_AC_AE*_HEquation Native M_1493195070F܄܄Ole TCompObj~UiA@AHA*_D_E_E_A  x==t,y==t++2,0d"td"2 FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfoWOlePres000Equation Native X_1493195069}F܄3T5 ^ x.  `0. & MathType &.00- @ Trebuchet MS!Iv@Lvfg-C2 (In Exercises 45 48, convert from radians~~s~t!@ Trebuchet MS!Iv@Lvfg-2  to degrees or<2@ Trebuchet MS!Iv@Lvfg-$2 degrees to radians.~9@ Trebuchet MS!Iv@Lvfg-2 45.46.2.55P @ Trebuchet MS!Iv@Lvfg- 2 3y9@ Trebuchet MS!Iv@Lvfg-2 47.4048.458!@ Trebuchet MS!Iv@Lvfg-C2 (In Exercises 49 51, solve the equation ~~~ @ Trebuchet MS!Iv@Lvfg-"2 graphically in the~~@+@ Trebuchet MS!Iv@Lvfg-2 given interval.~~9@ Trebuchet MS!Iv@Lvfg-2 49.sin0.6,02~%$@ Trebuchet MS!Iv@Lvfg-2 50.cosB@ Trebuchet MS!Iv@Lvfg- 2 xx %@ Trebuchet MS!Iv@Lvfg- 2 xx@Euclid Symbol!Iv@Lvfg- 2 px 2 px @Euclid Symbol!Iv@Lvfg- 2 -x@$ 2 -x 2 -xz 2 -xt 2 =c@ Trebuchet MS!Iv@LvfP- 2 a5b0 0 @ Trebuchet MS!Iv@LvfP- 2 fxx?i j @ Trebuchet MS!Iv@LvfP- 2 fxfx<@ Trebuchet MS!Iv@LvfP- 2 fx/= @ Trebuchet MS!Iv@LvfP- 2 xxj @ Trebuchet MS!Iv@LvfP- 2 fxfxx@Euclid Symbol!Iv@LvfP- 2 =- 2 ==-x 2 =- 2 =-=a&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 11 - 14, find all real solutions to the equations.11. fx()==x 2 "-5 a() fx()==4           b()   fx()=="-612. fx()== 1x a() fx()=="-5   b() fx()==0 & -"SystemfP 8-NANI- 14, find all real solutions to the equations.11. fx()==x 2 "-5 a() fx()==4           b()   fx()=="-612. fx()== 1x a() fx()=="-5   b() fx()==0 FMathType 6.0 Equation MathTyOle CompObjiObjInfoOlePres0002pe EFEquation.DSMT49q1d7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  13. fx()== x++7   a() f.S .  @`* & MathType& * BEuclid Symbol!TIv@Lvfq- 2 (yBEuclid Symbol!TIv@Lvfq- 2 )y- K  `. `--$  W  & UUk7 k  ? " -DEuclid Symbol!LIv@Lvfq- 2 (yDSEuclid Symbol!LIv@Lvfq- 2 )yDr Euclid Symbol!LIv@Lvfq- 2 (yD/ Euclid Symbol!LIv@Lvfq- 2 )yDEuclid Symbol!LIv@Lvfq- 2 (yDS!Euclid Symbol!LIv@Lvfq- 2 )yDr%Euclid Symbol!LIv@Lvfq- 2 (yD/'Euclid Symbol!LIv@Lvfq- 2 )yaEuclid Symbol!LIv@Lvfq- 2 (yaEuclid Symbol!LIv@Lvfq- 2 )y K  . -$  W  & tt7   ? " -cEuclid Symbol!TIv@Lvfq- 2 (ycSEuclid Symbol!TIv@Lvfq- 2 )ycr Euclid Symbol!TIv@Lvfq- 2 (yc/ Euclid Symbol!TIv@Lvfq- 2 )yc9Euclid Symbol!TIv@Lvfq- 2 (ycEuclid Symbol!TIv@Lvfq- 2 )yc Euclid Symbol!TIv@Lvfq- 2 (yc"Euclid Symbol!TIv@Lvfq- 2 )y4  Trebuchet MS!Iv@Lvfq- 2 3y#@ Trebuchet MS!Iv@Lvfq- 2 13.7$ %c@ Trebuchet MS!Iv@Lvfq- 2 a4b10  B@ Trebuchet MS!Iv@Lvfq- 2 14.1 Dc@ Trebuchet MS!Iv@Lvfq- 2 a2b3 ) #@ Trebuchet MS!Iv@Lvfq- 2 fxx%j @ Trebuchet MS!Iv@Lvfq- 2 fxfx9B@ Trebuchet MS!Iv@Lvfq- 2 fxxDj @ Trebuchet MS!Iv@Lvfq- 2 fxfx#x@Euclid Symbol!Iv@Lvfq- 2 =+ % 2 ==Bx 2 =-D 2 =-=&XAppsMFCC11Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  13. fx()== x++7   a() fx()==4    b() fx()==114. fx()== x"-1 3  a() fx()=="-2   b() fx()==3 & --"Systemfq 8-NANIEquation Native M_1493194149FPcPcOle CompObjix()==4    b() fx()==114. fx()== x"-1 3  a() fx()=="-2   b() fx()==3  FMathType 6.0 Equation MathType EFEquation.DSMT49q$T7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In ObjInfoOlePres000Equation Native @_1493194225F&&m:i'F  +.  #5 & MathTypep&4# -Y-!E%]%|%e%e{&--$ C%d% %c%_{&_{&k%k%|%|W%G%$- ; Trebuchet MS!Iv@Lvf- 2 2yh% Trebuchet MS!Iv@Lvf- 2 2y Trebuchet MS!Iv@Lvf- 2 3y& Trebuchet MS!Iv@Lvf- 2 35#@ Trebuchet MS!Iv@Lvf-C2 (In Exercises 1517, evaluate the expressi~~ !@ Trebuchet MS!Iv@Lvf-+2 on. Round your answers P52@ Trebuchet MS!Iv@Lvf-%2 to 3 decimal places.~s1@ Trebuchet MS!Iv@Lvf-2 15.516.3 @ Trebuchet MS!Iv@Lvf- 2 17.3@ Trebuchet MS!Iv@Lvf-C2 (In Exercises 18 20, solve the equation.~~~ @ Trebuchet MS!Iv@Lvf-'2  Round your answers P 2@ Trebuchet MS!Iv@Lvf-%2 to 4 decimal places.~s@ Trebuchet MS!Iv@Lvf-2 18.1719.@ Trebuchet MS!Iv@Lvf- 2 xx$ Euclid Symbol!Iv@Lvf- 2 -x @Euclid Symbol!Iv@Lvf- 2 -xz 2 -x 2 ==# y Trebuchet MS!Iv@Lvf- 2 1.5ha5" Trebuchet MS!Iv@Lvf- 2 10,@ Trebuchet MS!Iv@Lvf- 2 24"2@ Trebuchet MS!Iv@Lvf-2 20.1.4567 "@ Trebuchet MS!Iv@Lvf- 2 x4"J@Euclid Symbol!Iv@Lvf- 2 =4+&KAppsMFCC$$Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 15"-17, evaluate the expression.  Round your answers to 3 decimal places.15. 5  23       16. 3  2  17. 3 "-1.5 In Exercises 18 "- 20, solve the equation.  Round your answers to 4 decimal places.18. x 3 ==17      19. x 5 ==2420. x 10 ==1.4567 & --"Systemf 8-NANIExercises 15"-17, evaluate the expression.  Round your answers to 3 decimal places.15. 5  23       16. 3  2  17. 3 "-1.5 In Exercises 18 "- 20, solve the equation.  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P==$500,  r==4.75%,  n==5years22. P==1000,  r==6.3%,  n==3yearsIn Exercises 23 and 24, simplify the exponential expression.23.  x "-3 y 2 () 2 x 4 y 3 () 3        24.  a 3 b "-2 c 4 () 2  a 4 c "-2 b 3 () "-1 & -"Systemf+ 8-NANIEquation Native _1493194754F&Ole CompObji      !"#$%&),-./0123456789:;<?BCDEFGHIJKLMNOPQRSTUVWX[^_`abcdefghijklmnopqrstuvwz}~investing P dollars forn years with the interest rate r compounded annually.21. P==$500,  r==4.75%,  n==5years22. P==1000,  r==6.3%,  n==3yearsIn Exercises 23 and 24, simplify the exponential expression.23.  x "-3 y 2 () 2 x 4 y 3 () 3        24.  a 3 b "-2 c 4 () 2  a 4 c "-2 b 3 () "-1 FMathType 6.0 Equation MathType EFEquation.DSMT49q#l7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid ExtraObjInfoOlePres000@Equation Native ?_1493194830F@B2 G *.  `-< & MathType &@<'- Euclid Symbol!LIv@Lvf- 2 (y"Euclid Symbol!LIv@Lvf- 2 )y&#Euclid Symbol!LIv@Lvf- 2 (y&Euclid Symbol!LIv@Lvf- 2 )y F"Euclid Symbol!LIv@Lvf- 2 (y 'Euclid Symbol!LIv@Lvf- 2 )y\ Euclid Symbol!LIv@Lvf- 2 (y%Euclid Symbol!LIv@Lvf- 2 )y@ Trebuchet MS!Iv@Lvf-C2 (In Exercises 25 27, write an equation f~~P~~ @ Trebuchet MS!Iv@Lvf-2 or the line.~l2@ Trebuchet MS!Iv@Lvf-C2 (27.the line through the points 1, 8 and ~~Il#@ Trebuchet MS!Iv@Lvf- 2 4, 3 2@ Trebuchet MS!Iv@Lvf-C2 (28.the horizontal line through the point~~~ !@ Trebuchet MS!Iv@Lvf-2  3, 4e2@ Trebuchet MS!Iv@Lvf-C2 (29.the vertical line through the point 2~~~l!@ Trebuchet MS!Iv@Lvf- 2 , 3>q @ Trebuchet MS!Iv@Lvf-2 In Exercises ~~z @Euclid Symbol!Iv@Lvf- 2 -y `% 2 -y}# 2 -y-     c$ S& $( * Trebuchet MS!Iv@Lvf- 2 222F+ Trebuchet MS!Iv@Lvf- 2 2y  @ Trebuchet MS!Iv@Lvf-C2 (30 -32, find the - and -intercepts of th~sz~ )@ Trebuchet MS!Iv@Lvf-+2 e graph of the relation.~ +@ Trebuchet MS!Iv@Lvf-2 30.131.1  N"k@ Trebuchet MS!Iv@Lvf-2 916169Gb,+@ Trebuchet MS!Iv@Lvf-2 32.216 @ Trebuchet MS!Iv@Lvf- 2 xy@ Trebuchet MS!Iv@Lvf- 2 xyxy-S,@ Trebuchet MS!Iv@Lvf- 2 yx @Euclid Symbol!Iv@Lvf- 2 +=-=)I(, 2 =+*&JAppsMFCC##Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 25 "- 27, write an equation for the line.27. the line through the points 1, 8() and 4, 3()28. the horizontal line through the point 3, "-4()29. the vertical line through the point 2, "-3()In Exercises 30 -32, find the x- and y-intercepts of the graph of the relation.30.  x 2 9++ y16==1    31.  x 2 16"- y 2 9==132. 2y 2 ==x++1 & -"Systemf 8-NANI!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 25 "- 27, write an equation for the line.27. the line through the points 1, 8() and 4, 3()28. the horizontal line through the point 3, "-4()29. the vertical line through the point 2, "-3()In Exercises 30 -32, find the x- and y-intercepts of the graph of the relation.30.  x 2 9++ y16==1    31.  x 2 16"- y 2 9==132. 2y 2 ==x++1Ole 'CompObj(iObjInfo*OlePres000Sv FMathType 6.0 Equation MathType EFEquation.DSMT49qTT7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  35. Solve for t..A4  C.    ; & MathType&: Euclid Symbol!LIv@LvfW- 2 (ySEuclid Symbol!LIv@LvfW- 2 )y9-Euclid Symbol!LIv@LvfW- 2 (y.Euclid Symbol!LIv@LvfW- 2 )ypEuclid Symbol!LIv@LvfW- 2 (ypSEuclid Symbol!LIv@LvfW- 2 )y-g  t _w _J --$ c   Bo TJ TJ j j t t k -Euclid Symbol!LIv@LvfW- 2 (ySEuclid Symbol!LIv@LvfW- 2 )y3g   w J -$ c -  o J J     &k 9-HEuclid Symbol!TIv@LvfW- 2 (yHEEuclid Symbol!TIv@LvfW- 2 )yg  L 7w 7M -$ c  s o ,M ,M B B L L k --ii  Trebuchet MS!Iv@LvfW- 2 2y  Trebuchet MS!Iv@LvfW- 2 2y`  Trebuchet MS!Iv@LvfW- 2 2y+@ Trebuchet MS!Iv@LvfW-2 35.Solve for .4ec@ Trebuchet MS!Iv@LvfW-2 a235b321 +@ Trebuchet MS!Iv@LvfW-C2 (36.For what values of is each equation P~~ "@ Trebuchet MS!Iv@LvfW-2 true?Qc@ Trebuchet MS!Iv@LvfW- 2 ay\@ Trebuchet MS!Iv@LvfW- 2 by)j@ Trebuchet MS!Iv@LvfW- 2 c42!7 @ Trebuchet MS!Iv@LvfW- 2 tyeQ @ Trebuchet MS!Iv@LvfW- 2 xtyt$ @ Trebuchet MS!Iv@LvfW- 2 ayQ @ Trebuchet MS!Iv@LvfW- 2 aa @ Trebuchet MS!Iv@LvfW- 2 aaC) @ Trebuchet MS!Iv@LvfW- 2 aa e @Euclid Symbol!Iv@LvfW-2 +=--=-R#RQ 2 =a 2 =) 2 =C&{AppsMFCCTTDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  35. Solve for t. a() 2x++3t=="-5      b() 3y"-2t=="-136. For what values of a is each equation true? a()  a 2 ==a     b()  a 2 ==a    c()  4a 2 ==2a& & --"SystemfW 8-NANIEquation Native +p_1493194802F@@Ole =CompObj>i a() 2x++3t=="-5      b() 3y"-2t=="-136. For what values of a is each equation true? a()  a 2 ==a     b()  a 2 ==a    c()  4a 2 ==2a FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfo@OlePres000bEquation Native A_1493194894F@pd7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 33 and 34, determine whether =l 6  .    8 & MathType&7  Euclid Symbol!LIv@Lvf7- 2 (y SEuclid Symbol!LIv@Lvf7- 2 )y 9 Euclid Symbol!LIv@Lvf7- 2 (y Euclid Symbol!LIv@Lvf7- 2 )y Euclid Symbol!LIv@Lvf7- 2 (y SEuclid Symbol!LIv@Lvf7- 2 )y 9Euclid Symbol!LIv@Lvf7- 2 (y Euclid Symbol!LIv@Lvf7- 2 )y 9-Euclid Symbol!LIv@Lvf7- 2 (y .Euclid Symbol!LIv@Lvf7- 2 )y-| x2| 35Euclid Symbol!TIv@Lvf7- 2 (y5SEuclid Symbol!TIv@Lvf7- 2 )y59 Euclid Symbol!TIv@Lvf7- 2 (y5^ Euclid Symbol!TIv@Lvf7- 2 )y5Euclid Symbol!TIv@Lvf7- 2 (y5SEuclid Symbol!TIv@Lvf7- 2 )y59Euclid Symbol!TIv@Lvf7- 2 (y5Euclid Symbol!TIv@Lvf7- 2 )y59-Euclid Symbol!TIv@Lvf7- 2 (y5.Euclid Symbol!TIv@Lvf7- 2 )y51Euclid Symbol!TIv@Lvf7- 2 (y5J6Euclid Symbol!TIv@Lvf7- 2 )yH Trebuchet MS!Iv@Lvf7- 2 22 Trebuchet MS!Iv@Lvf7- 2 22- Trebuchet MS!Iv@Lvf7- 2 22@ Trebuchet MS!Iv@Lvf7-C2 (In Exercises 33 and 34, determine whethe~~s~P !@ Trebuchet MS!Iv@Lvf7--2 r the given points lie onR~~~B2@ Trebuchet MS!Iv@Lvf7-.2 the graph of the relation.~+@ Trebuchet MS!Iv@Lvf7-2 33.23 2@ Trebuchet MS!Iv@Lvf7- 2 12 c@ Trebuchet MS!Iv@Lvf7-2 a1,1b1,1c,2d  H 2@ Trebuchet MS!Iv@Lvf7- 2 22O+@ Trebuchet MS!Iv@Lvf7-2 34.918427c@ Trebuchet MS!Iv@Lvf7-2 a1,3b1,3c1,3d" k"@ Trebuchet MS!Iv@Lvf7- 2 xyyOO@ Trebuchet MS!Iv@Lvf7- 2 xxy8|@Euclid Symbol!Iv@Lvf7- 2 += 1 2 j Z7 2  1 2   2 ---P Z7 2 H 1 2  Z7 2  1 2 C 1 2 O 2 -+=Pn 2 -- & AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 33 and 34, determine whether the given points lie onthe graph of the relation.33. 2x 2 y++y 2 ==3 a() 1,1()   b() "-1,"-1()   c()  12,"-2()34. 9x 2 "-18x++4y 2 ==27 a() 1,3()   b() 1,"-3()   c() "-1,3() & -"Systemf7 8-NANIthe given points lie onthe graph of the relation.33. 2x 2 y++y 2 ==3 a() 1,1()   b() "-1,"-1()   c()  12,"-2()34. 9x 2 "-18x++4y 2 ==27 a() 1,3()   b() 1,"-3()   c() "-1,3() FMathType 6.0 Equation MathType EFEquation.DSMT49qËd7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHOle YCompObjZiObjInfo\OlePres000s:>j# | ^.   8 & MathType&8 Euclid Symbol!LIv@Lv f?- 2 (ySEuclid Symbol!LIv@Lv f?- 2 )y9$Euclid Symbol!LIv@Lv f?- 2 (y%Euclid Symbol!LIv@Lv f?- 2 )y9Euclid Symbol!TIv@Lv f?- 2 (y9SEuclid Symbol!TIv@Lv f?- 2 )y99$Euclid Symbol!TIv@Lv f?- 2 (y9%Euclid Symbol!TIv@Lv f?- 2 )y@ Trebuchet MS!Iv@Lv f?-C2 (In Exercises 41 44, find the points of ~~~~@ Trebuchet MS!Iv@Lv f?-72 intersection of the two curves. ~~P=@ Trebuchet MS!Iv@Lv f?-B2 'Round your answers to 2 decimal places. P~s9@ Trebuchet MS!Iv@Lv f?-2 41.23,59@ Trebuchet MS!Iv@Lv f?-2 42.35,3?9@ Trebuchet MS!Iv@Lv f?-2 43.a2,3b2,1N[#9@ Trebuchet MS!Iv@Lv f?-2 44.a,4b,1N= xD #%  Trebuchet MS!Iv@Lv f?- 2 xxM  Trebuchet MS!Iv@Lv f?- 2 xx@ Trebuchet MS!Iv@Lv f?- 2 yxyJe@ Trebuchet MS!Iv@Lv f?- 2 yxy}Dz\ @ Trebuchet MS!Iv@Lv f?- 2 yyyy_!_\ @ Trebuchet MS!Iv@Lv f?-2 yeyyeynLnM Euclid Symbol!Iv@Lv f?- 2 --z @Euclid Symbol!Iv@Lv f?- 2 -- 2 =-=s2 =-+=-z 2 ====-_!_ 2 ====-4L4^&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 41 "- 44, find the points of intersection of the two curves. Round your answers to 2 decimal places.41. y==2x"-3,y==542. y=="-3x++5,y=="-343. a() y==2 x ,y==3    b() y==2 x ,y=="-144. a() y==e "-x ,y==4    b() y==e "-x ,y=="-1 & "System? f? 8-NANIEquation Native ]_1493194856FOle xCompObjyiA*_D_E_E_A  In Exercises 41 "- 44, find the points of intersection of the two curves. Round your answers to 2 decimal places.41. y==2x"-3,y==542. y=="-3x++5,y=="-343. a() y==2 x ,y==3    b() y==2 x ,y=="-144. a() y==e "-x ,y==4    b() y==e "-x ,y=="-1 FMathType 6.0 Equation MathType EFEquation.DSMT49qZl7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In ObjInfo{OlePres000Equation Native |v_1493194937Fp4  F.  @/ & MathType&/+ BtEuclid Symbol!TIv@Lvft- 2 (yB1Euclid Symbol!TIv@Lvft- 2 )y-:``--$ :UUkkE/-B"Euclid Symbol!TIv@Lvft- 2 (yB#Euclid Symbol!TIv@Lvft- 2 )yEuclid Symbol!LIv@Lvft- 2 (yEuclid Symbol!LIv@Lvft- 2 )y Euclid Symbol!LIv@Lvft- 2 (y Euclid Symbol!LIv@Lvft- 2 )yEuclid Symbol!LIv@Lvft- 2 (y#Euclid Symbol!LIv@Lvft- 2 )yr$Euclid Symbol!LIv@Lvft- 2 (yc'Euclid Symbol!LIv@Lvft- 2 )y&Euclid Symbol!LIv@Lvft- 2 (y&Euclid Symbol!LIv@Lvft- 2 )y&r Euclid Symbol!LIv@Lvft- 2 (y&/ Euclid Symbol!LIv@Lvft- 2 )y&Euclid Symbol!LIv@Lvft- 2 (y&#Euclid Symbol!LIv@Lvft- 2 )y&r$Euclid Symbol!LIv@Lvft- 2 (y&/&Euclid Symbol!LIv@Lvft- 2 )yZ7' Trebuchet MS!Iv@Lvft- 2 2y Trebuchet MS!Iv@Lvft- 2 3y#@ Trebuchet MS!Iv@Lvft-@2 &In Exercises 37 40, let 1, 1, and ~~r A 2@ Trebuchet MS!Iv@Lvft-+2 evaluate the expression.~+@ Trebuchet MS!Iv@Lvft-2 37.138.76B +@ Trebuchet MS!Iv@Lvft-2 39.40.U#l@ Trebuchet MS!Iv@Lvft-2 fxxgxx%i@ Trebuchet MS!Iv@Lvft- 2 fggf`]@ Trebuchet MS!Iv@Lvft-2 fgxgfxHjG]\#z @Euclid Symbol!Iv@Lvft-2 -=-=+ % 2 -y@Euclid Extra!Iv@Lvft- 2 oo 2 ooF&AppsMFCCZZDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 37 "- 40, let   fx()== x"-1 3 ,  gx()==x 2 ++1, and evaluate the expression.37. f"og()1()    38. g"of()"-7()39. f"og()x()    40. g"of()x()F & --"Systemft 8-NANIExercises 37 "- 40, let   fx()== x"-1 3 ,  gx()==x 2 ++1, and evaluate the expression.37. f"og()1()    38. g"of()"-7()39. f"og()x()    40. g"of()x() FMathType 6.0 Equation MathTyOle CompObjiObjInfoOlePres000pe EFEquation.DSMT49qþT7T 7DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 45"- 48, convert 3T5 ^ x.  `0. & MathType &.00- @ Trebuchet MS!Iv@Lvfg-C2 (In Exercises 45 48, convert from radians~~s~t!@ Trebuchet MS!Iv@Lvfg-2  to degrees or<2@ Trebuchet MS!Iv@Lvfg-$2 degrees to radians.~9@ Trebuchet MS!Iv@Lvfg-2 45.46.2.55P @ Trebuchet MS!Iv@Lvfg- 2 3y9@ Trebuchet MS!Iv@Lvfg-2 47.4048.458!@ Trebuchet MS!Iv@Lvfg-C2 (In Exercises 49 51, solve the equation ~~~ @ Trebuchet MS!Iv@Lvfg-"2 graphically in the~~@+@ Trebuchet MS!Iv@Lvfg-2 given interval.~~9@ Trebuchet MS!Iv@Lvfg-2 49.sin0.6,02~%$@ Trebuchet MS!Iv@Lvfg-2 50.cosB@ Trebuchet MS!Iv@Lvfg- 2 xx %@ Trebuchet MS!Iv@Lvfg- 2 xx@Euclid Symbol!Iv@Lvfg- 2 px 2 px @Euclid Symbol!Iv@Lvfg- 2 -x@$ 2 -x 2 -xz 2 -xt 2 = [.  `;&@;$ & MathType` q5Euclid Symbol@wIw @wf- 2 (y:Euclid Symbol@wIw @wf- 2 )y! Euclid Symbol@wIw @wf- 2 (y! Euclid Symbol@wIw @wf- 2 )y-      Euclid Symbol@wIw @wf- 2 (yEuclid Symbol@wIw @wf- 2 )y/// / jEuclid Symbol@wIw @wf- 2 (yjEuclid Symbol@wIw @wf- 2 )ylEuclid Symbol@wIw @wf- 2 (ylEuclid Symbol@wIw @wf- 2 )y@@ Trebuchet MS@wIw @wf-C2 (You may use a graphing calculator to sols~ @ Trebuchet MS@wIw @wf-.2 ve the following problems.P~so@ Trebuchet MS@wIw @wf-C2 (1.Which of the following gives an equati~P~~o"@ Trebuchet MS@wIw @wf-12 on for the line through 3, 1~eUJ+@ Trebuchet MS@wIw @wf-12 and parallel to the line:21?~x @ Trebuchet MS@wIw @wf- 2 177 @ Trebuchet MS@wIw @wf- 2 A7^ @ Trebuchet MS@wIw @wf- 2 22P@ Trebuchet MS@wIw @wf- 2 15@ Trebuchet MS@wIw @wf- 2 B5@ Trebuchet MS@wIw @wf- 2 220K@ Trebuchet MS@wIw @wf- 2 C25PbM@ Trebuchet MS@wIw @wf- 2 D2Jn@ Trebuchet MS@wIw @wf- 2 yxR @ Trebuchet MS@wIw @wf- 2 yxL@ Trebuchet MS@wIw @wf- 2 yxLK@ Trebuchet MS@wIw @wf- 2 yxBM@ Trebuchet MS@wIw @wf- 2 yxRo8@Euclid Symbol@wIw @wf- 2 -xJ 2 =-+  2 =+L 2 =->K 2 =-+M 2 =-nEuclid Symbol@wIw @wf- 2 (-nEuclid Symbol@wIw @wf- 2 )-M @ Trebuchet MS@wIw @wf- 2 7-O@ Trebuchet MS@wIw @wf- 2 E21O@ Trebuchet MS@wIw @wf- 2 yxRMY @Euclid Symbol@wIw @wf- 2 -xO 2 =-+[&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  You may use a graphing calculator to solve the following problems.1. Which of the following gives an equation for the line through 3, "-1()and parallel to the line:y=="-2x++1?A() y== 12x++ 72     B() y== 12x"- 52     C() y=="-2x++5D() y=="-2x"-7E() y=="-2x++1 & N-"Systemf !-NANIEquation Native _1306129643FVVOle CompObjiA*_D_E_E_A  You may use a graphing calculator to solve the following problems.1. Which of the following gives an equation for the line through 3, "-1()and parallel to the line:y=="-2x++1?A() y== 12x++ 72     B() y== 12x"- 52     C() y=="-2x++5D() y=="-2x"-7E() y=="-2x++1 FMathType 6.0 Equation MathType EFEquation.DSMT49q¢PRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  2. ObjInfoOlePres000nEquation Native _1306131297FV/&, .  @+&+ & MathType 3Euclid Symbol@wIw @wfv- 2 (y Euclid Symbol@wIw @wfv- 2 )yEuclid Symbol@wIw @wfv- 2 (yNEuclid Symbol@wIw @wfv- 2 )yEuclid Symbol@wIw @wfv- 2 (yEuclid Symbol@wIw @wfv- 2 )y~Euclid Symbol@wIw @wfv- 2 (yEuclid Symbol@wIw @wfv- 2 )yEuclid Symbol@wIw @wfv- 2 (yEuclid Symbol@wIw @wfv- 2 )y Euclid Symbol@wIw @wfv- 2 (y Euclid Symbol@wIw @wfv- 2 )y!Euclid Symbol@wIw @wfv- 2 (y!Euclid Symbol@wIw @wfv- 2 )y#Euclid Symbol@wIw @wfv- 2 (y#Euclid Symbol@wIw @wfv- 2 )y%Euclid Symbol@wIw @wfv- 2 (y%Euclid Symbol@wIw @wfv- 2 )y1d  Trebuchet MS@wIw @wfv- 2 2y2@ Trebuchet MS@wIw @wfv-62 2.If 1 and 21,which of the ~ P~@ Trebuchet MS@wIw @wfv-$2 following gives 2?P~~=@ Trebuchet MS@wIw @wfv- 2 A2 @ Trebuchet MS@wIw @wfv- 2 B5@ Trebuchet MS@wIw @wfv- 2 C9@ Trebuchet MS@wIw @wfv- 2 D10@ Trebuchet MS@wIw @wfv- 2 E15+@ Trebuchet MS@wIw @wfv-2 fxxgxxi Ws@ Trebuchet MS@wIw @wfv- 2 fg` @Euclid Symbol@wIw @wfv- 2 =+=- @Euclid Extra@wIw @wfv- 2 og&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  2. If fx()==x 2 ++1   and   gx()==2x"-1,which of the  following gives  f"og()2()?A() 2  B() 5  C() 9  D() 10  E() 15 & N"Systemvfv !-NANI      !"#$%&'()*+,-./0123458;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqstuvwxyz{|}~If fx()==x 2 ++1   and   gx()==2x"-1,which of the  following gives  f"og()2()?A() 2  B() 5  C() 9  D() 10  E() 15 FMathType 6.0 Equation MathType EFEquation.DSMT49qPRDSMT6WinAllBasicCodePagesOle CompObjiObjInfoOlePres000VB  }.  <&<J & MathType + Symbol 5@wIw @wffw- 2 (y/ Symbol @wIw @wffw- 2 )y@ Symbol 6@wIw @wffw- 2 (yC Symbol !@wIw @wffw- 2 )y + Symbol 7@wIw @wffw- 2 (y  Symbol "@wIw @wffw- 2 )y 9 Symbol 8@wIw @wffw- 2 (y  Symbol #@wIw @wffw- 2 )y*  Trebuchet MS@wIw @wffw- 2 2y@@ Trebuchet MS@wIw @wffw-C2 (You should solve the following problems P~sL @ Trebuchet MS@wIw @wffw-=2 $without using a graphing caluclator.P~~~f9@ Trebuchet MS@wIw @wffw-C2 (4. Which of the following is the domain~P~~s~f@ Trebuchet MS@wIw @wffw-2 of ()log3?I8c@ Trebuchet MS@wIw @wffw-2 (A) , ` @ Trebuchet MS@wIw @wffw-2 (B) ,3] @ Trebuchet MS@wIw @wffw-2 (C) 3, }6@ Trebuchet MS@wIw @wffw-2 (D) [3,)w@ Trebuchet MS@wIw @wffw-2 (E) (,3]{fK"@ Trebuchet MS@wIw @wffw- 2 fxx(sf%@Symbol )T@wIw @wffw- 2 =-+>p~c 2 ->`  2 -]  2 -6 2 - 2 -Q}&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  You should solve the following problems without using a graphing caluclator.4.  Which of the following is the domain of f(x)=="-log 2 x++3()?(A) "-","()(B) "-",3()(C) "-3,"()(D) ["-3,")(E) ("-",3] & N"Systemwffw !-NANIEquation Native _1306129699F AOle CompObjiTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  You should solve the following problems without using a graphing caluclator.4.  Which of the following is the domain of f(x)=="-log 2 x++3()?(A) "-","()(B) "-",3()(C) "-3,"()(D) ["-3,")(E) ("-",3] FMathType 6.0 Equation MathType EFEquation.DSMT49qPRDSMT6WinAllBasicCodePagesObjInfoOlePres000ZEquation Native _1306131362F A A&> .  `8& 8x & MathTypep  Euclid Symbol@wIw @wf- 2 (y Euclid Symbol@wIw @wf- 2 )y Euclid Symbol@wIw @wf- 2 (y Euclid Symbol@wIw @wf- 2 )yEuclid Symbol@wIw @wf- 2 (yEuclid Symbol@wIw @wf- 2 )yEuclid Symbol@wIw @wf- 2 (yEuclid Symbol@wIw @wf- 2 )y+@ Trebuchet MS@wIw @wf-C2 (3.The half-life of a certain radioactive~~~~!@ Trebuchet MS@wIw @wf-32  substance is 8 hours. There~4@ Trebuchet MS@wIw @wf-C2 (are 5 grams present initially. Which ofs~~~~4#@ Trebuchet MS@wIw @wf--2  the following gives the ̅P~~@ Trebuchet MS@wIw @wf-C2 (best approximation when there will be 1 ~s~PP~5%@ Trebuchet MS@wIw @wf-2 gram remaining?ss~~ @ Trebuchet MS@wIw @wf- 2 A2 @ Trebuchet MS@wIw @wf- 2 B10@ Trebuchet MS@wIw @wf- 2 C15@ Trebuchet MS@wIw @wf- 2 D16Euclid Symbol@wIw @wf- 2 (2Euclid Symbol@wIw @wf- 2 )2@ Trebuchet MS@wIw @wf- 2 E19&AppsMFCCDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  3. The half-life of a certain radioactive substance is 8 hours.  There are 5 grams present initially.  Which of the following gives the  best approximation when there will be 1 gram remaining?A() 2  B() 10  C() 15  D() 16  E() 19 & N"Systemf !-NANITrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  3. The half-life of a certain radioactive substance is 8 hours.  There are 5 grams present initially.  Which of the following gives the  best approximation when there will be 1 gram remaining?A() 2  B() 10  C() 15  D() 16  E() 19 FMathType 6.0 Equation MathTyOle 6CompObj7iObjInfo9OlePres000: pe EFEquation.DSMT49q7  .  2&1 & MathType ( Symbol @wIw @wfm- 2 (y- Symbol @wIw @wfm- 2 )y9 Symbol @wIw @wfm- 2 (y< Symbol @wIw @wfm- 2 )y-f8fIfVf`$@ Trebuchet MS@wIw @wfm-C2 (5. Which of the following is the range o~P~~-@ Trebuchet MS@wIw @wfm-2 f ()5cos3?Ii$+@ Trebuchet MS@wIw @wfm-2 (A) , @ Trebuchet MS@wIw @wfm-2 (B) 2,4 @ Trebuchet MS@wIw @wfm-2 (C) 8,2  @ Trebuchet MS@wIw @wfm-2 (D) 2,8M@ Trebuchet MS@wIw @wfm- 2 28@ Trebuchet MS@wIw @wfm-2 (E) ,22I@ Trebuchet MS@wIw @wfm- 2 55Z @ Trebuchet MS@wIw @wfm- 2 fxxs\,@Symbol T@wIw @wfm- 2 p5#@Symbol T@wIw @wfm- 2 =++W 2 -@ 2 ZY@ 2 Z  2 - N 2 MT N 2 M  2 - U 2 FOU 2 F2 2 S 2 -|2 2 Sz2 2 S&AppsMFCCccDesign Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  5. Which of the following is the range of f(x)==5cosx++p()++3?(A) "-","()(B) 2,4[](C) "-8,2[](D) "-2,8[](E) "- 25, 85[] & N-"Systemfm !-NANIc<PRDSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  5. Which of the following is Equation Native r_1306131497F ApOle CompObjithe range of f(x)==5cosx++p()++3?(A) "-","()(B) 2,4[](C) "-8,2[](D) "-2,8[](E) "- 25, 85[] FMathType 6.0 Equation MathType EFEquation.DSMT49q=t  .   8&7L & MathType-h4h6 @ ObjInfoOlePres0004Equation Native H_1306135347MFpp     "' !#$%&43)*+,-./01295678F;<=>?@ABCDEGHKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~?N?U~2T 4@ Trebuchet MS@wIw @wdf- 2 3y+@ Trebuchet MS@wIw @wdf-C2 (6. Which of the following gives the solu~P~~&@ Trebuchet MS@wIw @wdf-"2 tion of tan-1 in ?~~ 4R5@ Trebuchet MS@wIw @wdf- 2 2yu@ Trebuchet MS@wIw @wdf- 2 (A) @ Trebuchet MS@wIw @wdf- 2 4y @ Trebuchet MS@wIw @wdf- 2 (B) n m@ Trebuchet MS@wIw @wdf- 2 4y@ Trebuchet MS@wIw @wdf- 2 (C)  @ Trebuchet MS@wIw @wdf- 2 3y;c@ Trebuchet MS@wIw @wdf- 2 3yS@ Trebuchet MS@wIw @wdf- 2 (D) @ Trebuchet MS@wIw @wdf- 2 4y9@ Trebuchet MS@wIw @wdf- 2 5y@ Trebuchet MS@wIw @wdf- 2 (E) L@ Trebuchet MS@wIw @wdf- 2 4y'@ Trebuchet MS@wIw @wdf- 2 xx 5@Symbol T@wIw @wdf- 2 px. 2 px] 2 px @ 2 pxN 2 px;5 2 px  2 pxu)@Symbol# T@wIw @wdf- 2 =u_ 2 -x&SAppsMFCC,,Design Science, Inc.DSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  6. Which of the following gives the solution of tanx==-1 in pd"xd" 3p2?(A) "- p4(B)  p4(C)  p3(D)  3p4(E)  5p4 & N-"Systemdf !-NANI,PRDSMT6WinAllBasicCodePagesTrebuchet MSSymbolCourier NewTimes New RomanMT Extra!O'_!!/G_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  6. 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Determine whether the graph of the function y==x  15  is symmetric about the y-axis, the origin or neither.4. Determine whether the function  y== x 4 ++1x 3 "-2x  is even, odd or neither. & N-"Systemcf: !-NANI=PRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  In Exercises 1 and 2, write an equation for the specified line.1. through 4, "-12() and parallel to 4x++3y==122. the line y==fx() where  f has the following values:3. Determine whether the graph of the function y==x  15  is symmetric about the y-axis, the origin or neither.4. Determine whether the function  y== x 4 ++1x 3 "-2x  is even, odd or neither. FMathType 6.0 Equation MathType EFEquation.DSMT49q„TPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid ExtraOle :CompObj;iObjInfo=OlePres000(p\8u.  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Identify the initial and terminal points, if any.  Indicate the direction in which the curve is traced. b() Find a Cartesian equation for a curve that contains   the parametrized curve.  What portion of the graph of the Cartesian equation   is traced by the parametrized curve? & N"Systemf !-NANIEquation Native >_1306135642;FǎOle aCompObjbi!OED/APFH_!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  8. x==5cost, y==2sint,0d"td"2pis a parametrization for a curve.   a() Graph the curve.  Identify the initial and terminal points, if any.  Indicate the direction in which the curve is traced. b() Find a Cartesian equation for a curve that contains   the parametrized curve.  What portion of the graph of the Cartesian equation   is traced by the parametrized curve? FMathType 6.0 Equation MathType EFEquation.DSMT49qPRDSMT6WinAllBasicCodePagesTrebuchet MSEuclid SymbolTimes New RomanEuclid Extra!OED/APFH_!APAE%B_AC_AE*_HA@AHObjInfodOlePres000:NEquation Native e1TablexK3$    .   !/&. & MathType y8 Euclid Symbol@wIw @wf- 2 (yyEEuclid Symbol@wIw @wf- 2 )yyIEuclid Symbol@wIw @wf- 2 (yyEuclid Symbol@wIw @wf- 2 )y Euclid Symbol@wIw @wf- 2 (y Euclid Symbol@wIw @wf- 2 )y+Euclid Symbol@wIw @wf- 2 (y+SEuclid Symbol@wIw @wf- 2 )yE\Euclid Symbol@wIw @wf- 2 (yE!\Euclid Symbol@wIw @wf- 2 )y+"Euclid Symbol@wIw @wf- 2 (y+d$Euclid Symbol@wIw @wf- 2 )yE&\Euclid Symbol@wIw @wf- 2 (yE+\Euclid Symbol@wIw @wf- 2 )y+z,Euclid Symbol@wIw @wf- 2 (y+7.Euclid Symbol@wIw @wf- 2 )yD Euclid Symbol@wIw @wf- 2 (yD SEuclid Symbol@wIw @wf- 2 )y? 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