Phat bi6u ndo sau ddy dfng Kh6ng c6 dillm cgc tiiiu, kh6ng c6 diiim qrc dai nao cua hhm sfr B... linghiQmcriaphucrngtrinh xs *xyo =yto +yu,timm6ili€nhQgitaxvdy B.
Trang 1
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CAu I :
Phuong trinh ti6p tuy6n cria ao tni nam s6 y ' = I!! x+2 tai A(-l; 3) c6 hQ s5 g6c li:
A.
CAu2:
B -1
B 1<-m
c -L:o2
Gi6 sri }I : ,f{x} c6 d4o him c6p hai trong khoirng (xe-h;xe+h), v6i h>0, Khi d6 ntiu f'{xo} : 0,f"{xo) > t}
thi:
xo h di6m kir6ng phdi ld diiSm csc ti6u
xomQt di,3m cUc dai
Cho y: xo Phat bitiu ndo sau dAy tlung
Hdm s5 d,5ng bi6n t6n R
Hdm s6 nghich bi6n tr6n kho6ng [-*; 0) va d6ng bi6n tr6n khoing (0; *m)
Him s6 nghich biiSn tr€n R
Hdm s6 ddng biiin tr6n khoing {-*;0} vA nghich biiin tr6n khodng (0; *m}
Tim n d6 dd thi hnm sO f(r) = x3 -rnx2 -x+m citnlc hodnhtai 3 di6m phdn biQt
B m*+7 C m<7
D 1
A.
C
CAu3:
A.
B
C
D
B xo mOt tti6m cFc tiiiu
D xo li di6m cgc ti6u vd cgc d4i
C&u4:
A.
CAu5:
= x-sinx tren [o;{]
Gi6 tri nh6 nhat, Icrn nhit cua him s6 / -
Dn luqt ld
0;1
m€,(
Tim rr d6 ttulng thing y = m c'at aO tli nam sO /(r) = x' _3xtqt 3 di€m phdn biQt
D m>7
D m>2hodcm <-,/.
- -a Cho ham so y : - ' r+1 co ti6 thi (C) Phuong ninh tr€p tuy6n cua d6 rh1 iC.1 r4i giao di€m cua no vor mrc hoanh ia
C zelR.
C 1<m<2
D oti
D' T=2x-7,
D .x : 1;y: 1
D.2
D m<0
D 1<m<2
A +-:-r*: '22'22"22 B }l :i : C ii::r-:
CAu 8 : Dudng tiQm cfn tlimg, ttulng tiQm c4n ngang cua AO tni nam ,6 y : 13 U
' l*x
C x:-1;]r:-1
0B.1c.3
Timt6t cLcic giittrici:r-m ae Uam s6 c6 3 cyc tri
A.
Ciu9:
A-B
C
D
CAu 10 :
A.
CAu Il :
A.
Ciu 12:
A.
CAU 13 :
A.
B
C
D
Ciu 14:
Cho f : f(x) xec dinh tr6n kho6ng(-car-?).N6u diAu ki€n sau duq c th6a m6n: lim*-,- * f {.x} : }s thi
Dulng thing x:ys Id ti€m c4n ngang cua d6 thi him s6 y : f(;)
Duong thing !I : ],s li tiem c?n ngang cua AO tiri nam sO y : f(r)
Eudng thing : : -ffi ld ti€m c{n dung cria d6 thi him s6 y : f{x}
Duong thing 5yeld tigm cin dimg cua aO tni nam tO y : ff-r)
sii ai6m cgc d4i cia hdm s61' : x{ - 2xt - 3 le:
m<2
Pt x' -3x-m = 0 c6 ba nghiQm ph6n biQt khi vi chi khi :
,1
Cho him s6 y : : ptr6t bi6u ndo sai t16y dring
Hdm s6 d6ng bitin tr6n khoing {-*;0} vd nghfch bii5n fi6n khoing (0; tm}
Hdm si5 nghich bi6n tr€n c6c khoang [-*;0] va {0; *co}
Hdm s6 nghich bi6n tr€n kho6ng {-*; tl} vd d6ng bi6n tr6n khoing (0; *m}
Him s6 d6ng biiin tren c6c khoing {-*;0i va {t}; -fimJ
Cho him s5 y : x3 + 3x2 - 4 c6 ad tiri (c) Phuong trinh ti6p tuy6n cua d6 thi (C) tai ditim c6 hoinh d0 beng
-3ld
Trang 216 To6n - r THPT TrAn HQi An
A.
CAu 15 :
A.
CAu 16:
A.
Ciu 17:
Tim m d6 hdm s6 sau: /(x) =! *' -*' +3x d4t cgc d4i tai x = I
J
^>Jj
Phuong trinh ducrng ti6m cin ngang cria aO thi hdm sii .11x; = t1
fa
9-x'
Tim n d6 him sii .f (*) = x +2m nghich bi6n trdn 2 khodng x6c dinh
x
C ,.!
2
C \A
c 1
D ,rJj
D m<0
D.2 D.0
A.
CAU 18:
A
CAU 21 :
A
Ciu22:
A
C
CAu 23:
m>0
Sti rtt6orchung cuaduimg theng y: x+l vdeO *i Uarns6: 7 = xt -3x' +4x+l Ii :
Cho y: xo Phat bi6u ndo sau ddy dfng
Kh6ng c6 dillm cgc tiiiu, kh6ng c6 diiim qrc dai nao cua hhm sfr
B *r!a
L
x:0 li di6m cyc ti6u cua him s6
Tit cdba ph6t bi€u tr6n d6u sai
x:0 ld dii5m cuc dai cria hirm s5
St5 tiiip tuy6n cua d6 thi hnm s6, ' - x x-1+ 2
)t'B )
Tqp CtLt4 cria hirm ,O 11-ry =
=1- J +r- fa
Lt ( o:;l 33 B (o;^ l
Chohims[t - Ite
InER
m<-f a1no m>f
"I;
Gi6 tri cuc ti6u cria him sd -f (*) = x4 -2x2ld
(FI)toog soagdudargtha"g Y:x li:
A.
Ciu 19:
A.
B
c.
D
Ciu 20 :
GiisuI:,f(x) c6d4ohimrr6nK.Ntiuf'(r) lA,Vx E ffvdft(r): OchitaimQts5htuh4ntti6mthi
hdm so f(x)
Ld him |eng tr6n K
D6ng bi6n tr6n K
ci6trinh6 nhit criahim s5 y : ,{x - Z + \E-tr6ndo4n [2;\1it
C [0;+ccJ
- 2tnx2 -:- 31 1m la tham sii) cia fir cua m ad iram s6 c6 s6 cuc da s6 cuc ti6u iA
B' *<-aboacm>1 rl3€
2Z
B Nghfch bi6n tr€n K
D D6ng bi6n vi nghich bi6n tr6n K
A.
C
Cilu}4z
A.
Ciu 25 :
A.
Ctu26 z
A.
B
c.
D
Cbu27:
Cho | : f(x) xac dinh tr6n D Ni5u di€u kiQn sau dugc th6a m6n: lim**r; f {*} : -m (xo E D} thi Duong thing 5-x6ld ti6m cin ngang cua aO tni nam s6 y : f {x}
Dudmg thing x="xr li tiQm c4n dimg cua dO thi him s(5 -y : f(r)
Duong thing 5-x6li tigm cfln dimg cria aO tni nam sO y : f (x)
Dudmg thing x: x6li tiQm cfn ngang cria tlii tt''i him s5 y : f txl.
.A Hirm s6 ) = - + 3 c6 ti€m cfln ngang c6 phuong trinh:
x A.
Ciu 28 :
Gie tri lon nhAt nho nhdt cua hdm s5 -f (*) = rtr- - i' lin lusr lil
D ):0
Trang 3cdrt 29r
od ttri ham s5 i = -x3 -3x2 -f 4 c(trb atil- chung voi fruc ox lir :
CAu 30 : Tim tdt ce circ gia tri cria z d6 him so
/(x) : x3 - xz f lzrr c6 cgc rri
i
A
nx<-^ J
1
B *ri
D 2;1 D.2
D !=x+l D.2
D 1
D / =-2x+3
D !=2x+3
D.3
D m<0
D.0
3 -_1
-f(x)=4 ,ui M(0;-l) tit
x+/.
Ciu 3l :
Phuong tinh ti6p tuy6n cria aO thi nam s6
+x-1
D *r l
-2cfuf.uc Ox tai sti diilm :
c, Y=-x+l
c.2
A
CAU 33 :
A
CAu 34 :
A
CAu 35 :
A
B
C
D
CAU 36 :
A
Cau i7 :
Pt x3 -3x +2 - m -Oc6 dring 1 nghiQm khi vir chikhi :
Aam<4 B 0<m<4 c m<4vm> 4 D m> 4
Timzdiihims6 -f(x)=x3 +(m+l)xz +mx+3 d4tcgctrit?r .rr )x2 saocho x,3 *xr3 -Q
Cho f : :c3 PhAt bi6u ndo sau d6y dring:
Him s6 nghich bi6n h€n R Hdm s6 d6ng bi€n tr6n R
Him s6 nghich bi6n r€n khoing [-*;0] vd ct6ng bi6n tr6n khoing {0; *m}
Hdm s6 tl6ng bi6n tr6n khoing (-*;0) vn nghich birin tr0n khoing {O; +mi
Tim m d6 gi6 tri cuc d4i cria hdm sti f (x) =3xo -.,1-5x' +3m bzng3
Him sr5 , f (x) =
h c6 s6 tiem can:
2B.3C.0 Cho (P) y = ,' -2* +3 PTTT cria (P) t4i giao ttiiSm vdi tr.uc Oy li:
Phucmg trinh tiiip tuy6n cua aO tni nam sO /(x) = x' , bi6t titip tuy6n c6 h0 s6 g6c b6ng 2 ]d
A.
Ciu 3E :
A.
Ciu 39 :
A.
Ciu 40 :
A
CLt42:.
t :
Him s6 : /ix) = vr' + I
c6 s6 ti€m cdn lir :
x
Ciu 44 : S6 dirim cyc tri cria him s6 F : s3 - 3r te:
A.1B.2
cAu 41
' Giarri nhd nhat cria hhm sti 71x; = , + I rr6n khoang (0; +oo) la
x
A xom0t tlii5m cyc tii5u cua him 16 ,f{x}
B xo ld mOt di6m qrc dai cria him .6 f{t}
C xold m$t tli6m kh6ng phni h tli6m cuc del cua him s6 f{:r}
D xold mOt tlirim cyc ct6i vd cpc ti6u cua Ue 6 f{x}
Cnu 43 : Tim tdt ci c6c gi6 fi cin m AC mm sO /(x) = x' +mx ttdng biiln n€n t0p x6c dinh cua n6
c.3
GiisuI = f{x}li6ntuctr6nkhoinglf = (:s - hx**h}vdc6daohimtrenKho4ctr6nK\{x6},vcrih>0.
Nriuf'{x} } 0tren}*ro6ng (ro -Iuxo}vaf'{x.} { Otrenkhoang {ro;xq * h}ttri
Trang 4T6 to6n - Trudns THPT TrAn
Ciu 45 : Cho him s6 1, : -x3 * 3x * 1 c6 d6 thi (C) Phuong trinh tii5p tuytin cua ao tni t4t diiim u6n cua (C) li:
3 CAu46: chohirmsiS],:
ir= + rnx? + (nr * 6)x- {rm + lj imtathamsS).Gi6tricuamd6hams5trcnadng
bi6n tr0n R ld
m]>3 C -?< rr { 3 D -3{m{2
Cho him s6 y : xz - 3x cO aO tiri (C) Dua vio tt6 th, (C), hiy cho bi6t voi phuong trinh tham s6 m:
-t3 - 3r * tn : 0 thi ph6t bi6u ndo sau diy dring:
m <2, phuong trinh c6 1 nghiQm B m >-2, phuong trinh c6 2 nghiQm
A.
Ciu47:
B nrd-3
A.
C
Ciu 48 :
A.
Ciu 49:
A.
CAU 50 :
A.
CAu 5l :
A.
Ciu 52 :
A.
CAu 55 :
A.
Ciu 56 :
A.
Ciu 57 :
A.
CAU 58 :
A.
-2<m<2,phuong.trinh c6 3 nghiQm -2, phuong trinh c6 I nghiQm
Trong c6c him s6 sau, hhm s6 ndo kh6ng c6 tli6m chung voi tryc Ox:
c y=x
A Jilv=*
C (C) kh6ng c6 tigm cQn
Cau 53 : HAm s6 ], : * aorrg bi6n tr6n:
.r+1
B' (C) luon cit tn:c hoanh
D' Hdm s5 khong c6 cuc tri
B Tdt cabakhoing tr6n tliiu sai D.2
D !=xa -x2 +
D v=2
D (-1;1)
D I
D R\{-1}
5 D
10
D 2,ti
D.3
D (2;+a)
Phuong trinh dulng tiQm c4n dimg cia OO tli fram sO /(x) = 2] fa
tn2
Him sr5 f G) = x3 + 3x d6ng bitin tr€n khoing nio sau dAy
!3 3jap 6n A, B C B (*;-r) vn fl;+oc) C
t,i d6u dring
Cho a +D :2 , GTNhI cua a' ub' lit:
4B.0C.2
Cho him s6, 1' = x' + mx' - x + 2 c6 OO tiri (C) Chqn phuong dn sai::
A
Ciu 54 :
Gi6 ut ion nh6t cua hdm s6 1' : :?Iil
- o€n doan IO; fl fa
- x*7
453
767
KhoAng c6ch gita hai cti6m cgc trj cua h/s : y = .r3 * 3 x2
Tim z d6 ti6m c6n dimg cria AO tli mm sti 71x; = 2'*l
di q*
x+m M(2;3)
a
-L
Him s6 y = xt -3x'
Him s6 y : ri3 - tr2 * 4x nghich bi6n tren:
2 {-2; 'J- -:)
?,
/_ ,\
\^t LJ
5
8.2C.0 nghich biiSn trEn l*roing nio sau tl0y,
C
y = 1 (,F1) sO tiiip tuyiin cia 116 thi hs (H) song soug rludmg theng y x tdi:
x-l A.3B.2c.or.,
CSru 60: -, Hims6 r - 4 -t-^ -2 j:x* -Zmx" -m+2 -,- , ^ cittrr"ox ! ^ teihaidi6mkhivdchikhi :
Trang 5CAu 61 : Gqi (-r:-r.) linghiQmcriaphucrngtrinh xs *xyo =yto +yu,timm6ili€nhQgitaxvdy
B (C) d6i ximg qua trgc Oy
D (C) lu6n cit t4rc hoanh
c I
c iCI; t)
c I
C ( co;l) vi (1;+*)
D m>2
D v =-J;
D.3
D r=0
D Y:9x- 26
D.2
D.3
D (-1; 1)
D VmeR
D 1<m
D.3
D (*;+*)
Ciru 62 :' SO Aiiim chung cua duong thing y = x vi ttd thi
8.0
B.4
Him s6lu6n c6 di6m cuc hi x:0
(O kn6ng c6 tiqm cin
A.2n.o
CAu 70 : Hirm sd ], = -ru + 2xs dOng bi5n n€n:
A ( *;-l) vn (-!+o) B (-1;l) Ciu 75 : Cho y = *' Phet bi6u nio sau tl6y dring
c' Y =J;
t X*2 ., tramso: !=; rut
c.2
A, CAu 63 :
A
CAU 64 :
Ducrng thdng qua 2 di6m cyc tt4i cira dii thi him s6 .f @) = -xo +2x2 lit
CAu 66 : Cho hdm s5 y : x3 - 3x c6 d6 thi (C) Phuong trinh tiilp tuy6n cria d6 thi (C), bilSt ti6p tuy6n d6 song song vdi
:X.t
Hdm s6: Y ' = 7-x co sO tipm c6n li:
CAu 65 : Gi6 tri lcrn nh6t, nh6 nhAt cria hhm s6 y = lxo - ar, - Sl
duong thing Y : 9r li
y: -9x+ 16 B r : -1, - -9 lg
GT LN cua hdm s6 )' = G-+J5-x ld :
2J'
c.2D.0 tr€ndo4n ?a;4lAnluCIld
c I =9x- 15
c J'
A.
Cilr67 z
A.
CAru 68 : A.
c.
Ciu 69 :
Cho hdm s5: y = mxo + x' -2 (m * 0) c6 dO thi (C) Chgn phuong 6n sai:
/=x3+3x2+8x+l (/1) si5ti6ptuy6n ciratl6ttrihs(H)songsongdulngthing y=x+28 ld:
CAu7l I x+Z
) - - (H) Outmg thang y: x + m cit d6 tbi (ID tai hai tti6m ph6n biQt ktri:
" x+l
Phuongtinh x3 +3xz -2-fi\.=Ac(t nghiQmduorng khi:
SO aiiim cyc tri cuahim s5: .), =cos2x h6n (0; Zn) U:
Him so -f (x) = jj d6ng bi€n tr€n khoing ndo sau d6y
x+1
A
Ctu72:
A.
Ciu 73 : A.
Cta74z
A' x:0 li di6m cgc ti6u cua him s6
B Kh6ng c6 di6m cyc ti6u, kfiOng c6 ttiiSm cuc tlai uao ci cria him s6
C x=0 li ttiaim cgc d4i cua him sti
D T6t c6 ba pMt bi6u tr6n ddu sai