17) y = log 4. 19) y = ) y = 23) f (x) = x 5 x 4 + 3x 3 3x 2 6x + 1. k = 0

Size: px

Start display at page:

Download "17) y = log 4. 19) y = ) y = 23) f (x) = x 5 x 4 + 3x 3 3x 2 6x + 1. k = 0"

Alexandra Myrtle McGee
5 years ago
Views:

1 Precalculus Assignment Evaluate each expression. Name ID: 1 Date Period 1) log 1 ) log 3) log 3 1 ) log 7 7 ) log 1 Expand each logarithm. ) ln (x ) 7) log (u v w ) ) log 9 (x z ) Condense each expression to a single logarithm. 9) log 11 + log 1 + log 7 10) log x + log Identif the domain and range of each. Then sketch the graph. 11) = log (x 1) + 1 1) = log 3 (x + 1) 3 (x + ) 13) = log 1 1) = log (x 1) 3 (x ) + 1) = log 1 Find the inverse of each function. 1) = log 1 ( x) 17) = log ( 3x) 1) = log (x + 3) 0) = x 19) = 10 1) = Determine whether the upper and lower bound tests indicate k is an upper bound, a lower bound, or neither bound on the real zeros of f (x). x 3 1 x ) f (x) = x 3 x + x + k = 3 ) f (x) = x + 3x + x 3 3x x + 3 k = 0 Find all zeros. 3) f (x) = x x + 3x 3 3x x + 1 k = 0 ) f (x) = 3x 3x + ) f (x) = x x + Factor each to linear and irreducible quadratic factors. One root has been given. 7) x + 1x x 30x 0 = 0; ] Lr0D1jB QKEuhthaY [SvoefqtkwOaSrgeW ulnl^cl.d u kaal[lq ZrJiegnhPtLsR lrzewsuerbvvedj.t q XMLaidQeA UwZirtGhG wipnmfxivnhictme^ ZPPrnedcoaVlnceulPuYs. Worksheet b Kuta Software LLC

2 ) x + x 3 + x 9x 7 = 0; 3 + i State the possible number of positive and negative zeros for each function. 9) f (x) = x x 3x 3 + 9x + 3x 19 30) f (x) = x + x + 3x 3 + x + x ) f (x) = x x x + 3 3) f (x) = x 1 Divide. Write our answer in fraction form. 33) (3x 1x x x 1) (x 3) 3) (x + 13x x x 3) (x + ) For each function: (1) state the maximum number of turns the graph could make, () determine the real zeros and state the multiplicit of an repeated zeros, (3) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, () describe the end behavior, and () sketch the graph. 3) f (x) = x 1x + x 3 x 3) f (x) = x 3x + x 37) f (x) = x + x + 9 3) f (x) = x 3 7x + 1x 9 39) f (x) = x + x x 3 + x x Find all roots. 0) x 13x + = 0 1) x 3 + x + x + = 0 State the possible rational zeros for each function. Then find all rational zeros. ) f (x) = x 3 9x x ) f (x) = x 3 + x x 1 ) f (x) = x 3 1x x + ) f (x) = x 3 + x + x + Divide. Write our answer in fraction form. ) (9x 3x + ) (x ) 7) (3x + 1x + x 3 1x + 11x + 1) (x + ) ) (x + 30x 3 x x + 1) (x + ) 9) (3x 9x 7x 3 + 9x 3x + ) (x 3) 0) (3x 9x + 3x 3 9x x + 3) (x 3) Evaluate f (x) at k. 1) f (x) = 3x 3 x x + k = Find the remainder when f (x) is divided b x k. 3) f (x) = x 3 x + x k = 1 ) f (x) = x 3 x x k = ) f (x) = x 3 7x + 10x k = Write a polnomial function of least degree with integral coefficients that has the given zeros. ) 3,, 1 ) 1 3 mult s uf0x1kz zkjuxtwae zsnoifatawsaqrwem FLFLECq.O v OAolpl[ qriihgrhftnsm iraelsmeurgvdemdv.t ] LMUaMdBeV dwxitt]h\ PIVnNfKiTnhiptLej bpgrqehceahlncoublnupss. Worksheet b Kuta Software LLC

3 Consider each power function. Determine the domain and range, intercepts, end behavior, continuit, and regions of increase and decrease. Then sketch the graph. 7) f (x) = x x 7 3 ) f (x) = x x 9) f (x) = x 9 x For each problem, find the average rate of change of the function over the given interval. 0) f (x) = x x + ; [, 9 ] 1) f (x) = x x + ; [0, 1 3 ] RG0q1ne UKuttoaW aswotfbtywbavr[e] `LSLKCH.P H aazlvlu ^rgieguhztdst RrJets\emrmvYeZdS.b [ MMtaOdMe_ dwmijtnhx KIZnYfDinPitses mpurdeaccaslfcwujlvulsl. -3- Worksheet b Kuta Software LLC

4 ) f (x) = x + ; [ 1, ] For each function, identif the holes, intercepts, horizontal asmptote, domain, limit behavior at all vertical asmptotes, and end behavior asmptote. Then sketch the graph. 3) f (x) = x x x x x ) f (x) = x + 3x + x + x + x State the possible rational zeros for each function. Then find all rational zeros. ) f (x) = x 3 3x 1x + 1 ) f (x) = x 3 3x 3x + Divide. Write our answer in fraction form. 7) (7x + 1x 3 17x 1) (x + 1) ) (7x + 11x 3 11x 1) (x + 1) Determine if d(x) is a factor of f (x). 9) f (x) = x 1x + 3x 3 + x + 9x + d(x) = x 70) f (x) = x x 1 d(x) = x + 1 H kc0m1mk vk[uwt\an hswoefttfwaacrteg cljlwcj.i S qael`l[ nrxi`gfhotwsi lr`eosremrrvuetd\.r o \MFaRdket mwmihtqhx mi`nyfmi[naiotfeg apurqeicla^lrcmurlkuwsb. -- Worksheet b Kuta Software LLC

5 Precalculus Assignment Evaluate each expression. Name ID: 1 Date Period 1) log 1 ) log 3) log 3 1 ) log ) log 1 3 Expand each logarithm. ) ln (x ) ln x + ln 7) log (u v w ) log u + log v + log w ) log 9 (x z ) log 9 x + log 9 + log 9 z Condense each expression to a single logarithm. 9) log 11 + log 1 + log 7 log (13 7 ) 10) log x + log log ( x ) Identif the domain and range of each. Then sketch the graph. 11) = log (x 1) ) = log 1 (x ) + 1) = log (x 1) 3 Domain: x > 1 Domain: x > x Domain: x > 1 x x 1) = log 3 (x + 1) 3 1) = log 1 v Bv0E1Je OKEu`txau esmozflt\wbamrxei RLPLOCT.k C oaglxls JrKiEgqhItYsh GrVeKsgeUrVvze_dL.A L DMXaFdGew VwRiItghn ]Ixntfpi[niQtLeT UPFrUeacSa_lJcwuOlKumsx. -1- (x + ) Find the inverse of each function. 1) = log 1 ( x) = x 17) = log ( 3x) = 3 1) = log (x + 3) = x 3 0) = x 19) = 10 = log x 1) = x 3 1 = log x 3 x = log 1 Domain: x > 1 Domain: x > x x x Determine whether the upper and lower bound tests indicate k is an upper bound, a lower bound, or neither bound on the real zeros of f (x). ) f (x) = x 3 x + x + k = 3 ) f (x) = x + 3x + x 3 3x x + 3 k = 0 Find all zeros. Lower bound 3) f (x) = x x + 3x 3 3x x + 1 k = 0 Neither x Neither { ) f (x) = 3x 3x +,, 3, } { ) f (x) = x x 10 +,,, 3 Factor each to linear and irreducible quadratic factors. One root has been given. 7) x + 1x x 30x 0 = 0; (x + )(x + 1)(x + x 10) = 0 Worksheet b Kuta Software LLC

6 ) x + x 3 + x 9x 7 = 0; 3 + i (x 3)(x + )(x + x + 13) = 0 State the possible number of positive and negative zeros for each function. 9) f (x) = x x 3x 3 + 9x + 3x 19 Possible # positive real zeros: 3 or 1 Possible # negative real zeros: or 0 30) f (x) = x + x + 3x 3 + x + x + 90 Possible # positive real zeros: 0 Possible # negative real zeros:, 3, or 1 31) f (x) = x x x + 3 Possible # positive 3) f real (x) = zeros: x 1 or Possible 0 # positive real zeros: 1 Divide. Write our answer in fraction Possible form. # negative real zeros: or Possible 0 # negative real zeros: 1 33) (3x 1x x x 1) (x 3) 3x 3 3) x + (xx + 13x x x 3) (x + ) x 3 + x x x 3 For each function: (1) state the maximum number of turns the graph could make, () determine the real zeros and state the multiplicit of an repeated zeros, (3) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, () describe the end behavior, and () sketch the graph. 3) f (x) = x 1x + x 3 x 37) f (x) = x + x ) f (x) = x + x x 3 + x x Find all roots. Max # turns: 3) f (x) = x 3x + x Real zeros: { 0 mult., 1 mult. 3 } Max # turns: 1 Real zeros: { 3 mult. x-int, } crosses: 1 x-int, crosses: None x-int, Max # turns: doesn't cross: x-int, 3doesn't cross: 0 Real zeros: {0, 1 mult. } End behavior: xend behavior: lim f (x) = x-int, crosses: 0 lim f (x) = x lim f (x) = x-int, lim f (x) = doesn't cross: 1 End behavior: lim f (x) = x lim f (x) = 3) f (x) = x 3 7x + 1x 9 0) x 13x + = 0 {,, 7, 7 } 1) x 3 + x + x + = 0 {, i, i} State the possible rational zeros for each function. Then find all rational zeros. Max # turns: Real zeros: { x-int, crosse Max x-int, doesn Real End behavio x-int lim x-int f (x) = x lim f End (x) = b lim x x lim ) f (x) = x 3 9x x + 30 Possible rational 3) zeros: f (x) = x 3 + x x 1 Possible rational zeros: ± 1, ±, ± 3, ±, ±, ± 10, ± 1, ± 30 ) f (x) = x 3 1x x + Possible rational ) zeros: f Rational zeros: { 3} (x) = x 3 + x + x + Possible rational Rational zeros: { 1 zeros Divide. Write our answer in fraction, 1, ± 1, ±, ± 3, form. ±, ± 1, ±, ± 3, ± ± 1, ±, ±, ± 1, ±, ± ) (9x Rational 3x + ) (x ) 9x zeros: {3} x 7 7) (3x + 1x + x 3 1x + 11x + 1) (x + ) 3x + x 3 x + x ) (x + 30x 3 x x + 1) (x + ) x 3 x + x + 9) (3x 9x 7x 3 + 9x 3x + ) (x 3) 3x 7x + x ) (3x 9x + 3x 3 9x x + 3) (x 3) 3x + 3x Evaluate f (x) at k. 1 x 3 x 3 Rational zeros: { } x + 1) f (x) = 3x 3 x x + k = Find the remainder when f (x) is divided b x k. ) f (x) = x 3 x x k = 3) f (x) = x 3 x + x k = 1 ) f (x) = x 3 7x + 10x k = Write a polnomial function of least degree with integral coefficients that has the given zeros. 0 ) 3,, 1 f (x) = 1x 3 + x + 3x + ) 1 3 mult. 3 f (x) = 7x3 7x + 9x 1 e ZD0D1xM IKDuJtDa_ qsbopf\tqw`avrte` alel^cm.x q haululo [rzibgehmtwsy vrneyshe[rnvfebdl.m ` DMlaPdLee [wbixt[hq NI^njfqiJnQiUtaec BPRrSeHcPaxl\cvuplkuzsI. -- Worksheet b Kuta Software LLC

7 Consider each power function. Determine the domain and range, intercepts, end behavior, continuit, and regions of increase and decrease. Then sketch the graph. 7) f (x) = x Domain: (, 0) (0, ) x Range: (0, ) No intercepts lim f (x) = 0 lim f (x) = 0 Infinite discontinuit at x = 0 Increasing: (, 0) Decreasing: (0, ) 7 3 ) f (x) = x Domain: (, 0) (0, ) x Range: (, 0) (0, ) No intercepts lim f (x) = 0 lim f (x) = 0 Infinite discontinuit at x = 0 Decreasing: (, 0), (0, ) 9) f (x) = x 9 Domain: (, 0) (0, ) x Range: (, 0) (0, ) No intercepts lim f (x) = 0 lim f (x) = 0 Infinite discontinuit at x = 0 Decreasing: (, 0), (0, ) For each problem, find the average rate of change of the function over the given interval. 0) f (x) = x x + ; [, 9 ] 13 1) f (x) = x x + ; [0, 1 3 ] 1 3 e K`0n1aD QK]u]tOa^ PS`oYfntuwuaNrMeL KL_LmCD.U L AAtlIlI wrji\gfhzthsg xrpeisie_rdvmeadj.f cmzatdzec RwPiJt[hg kidndfiiangihtkeb gp_rgepcxaolucutlqumsh. -3- Worksheet b Kuta Software LLC

8 ) f (x) = x + ; [ 1, ] 1 For each function, identif the holes, intercepts, horizontal asmptote, domain, limit behavior at all vertical asmptotes, and end behavior asmptote. Then sketch the graph. 3) f (x) = x x x x Holes: x = 0 Horz. Asm.: = 1 x-intercepts:, -intercept: None Domain: All reals except 0, 1 Vert. Asm. behavior: lim x 1 f (x) =, lim x 1 + f (x) = End behavior asm.: = 1 x ) f (x) = x + 3x + x + x + Holes: x = Horz. Asm.: = 1 x-intercepts: 1, -intercept: 1 3 Domain: All reals except 3, Vert. Asm. behavior: lim f (x) =, lim f (x) = x 3 x 3 + End behavior asm.: = 1 x State the possible rational zeros for each function. Then find all rational zeros. ) f (x) = x 3 3x 1x + 1 Possible rational ) zeros: f (x) = x 3 3x 3x + Possible rational zeros ± 1, ±, ± 3, ±, ± 9, ± 1, ± 1, ± 3, ± 9 Divide. Write our answer in fraction form. Rational zeros: {3} 10 Rational zeros: { 1,, 7) (7x + 1x 3 17x 1) (x + 1) 7x 3 + 9x ) 9x (7x + 11x 3 11x 1) (x + 1) 7x 3 + x x 7 Determine if d(x) is a factor of f (x). x + 1 9) f (x) = x 1x + 3x 3 + x + 9x + d(x) = x Yes 70) f (x) = x x 1 d(x) = x + 1 No p s[0q1sg rkvuttqan VS_owfqtawwafrKe] nlilicu.t C CAOlQlh ArYiEg^hrt]sW vrheasyeorrvrexdk.v J ]Mrakdges ZwfihtkhX eiannfoifndigtnen nprkemcdailuckuolaujsf. -- Worksheet b Kuta Software LLC

HONORS PRE-CALCULAUS ACP Summer Math Packet

Name Date Section HONORS PRE-CALCULAUS ACP Summer Math Packet For all incoming Honors Pre-Calculus ACP students, the summer math packet will be on the school website. Students will need to print a cop