I Tavi

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I <strong>Tavi</strong> gasaxseneblad! p(A) = m n , sadac m xdomilobis xelSemwyob SemTxvevaTa raodenobaa, xolo n yvela SesaZlo SemTxvevaTa ricxvi. 10 naxazze mocemulia y=f(x) funqciis grafiki. aRwereT, rogor vipovoT funqciis mniSvneloba, roca x=1; 3,5 da piriqiT rogor vipovoT x, Tu f(x)=4; 0; 1. ganvixiloT amocana: gaagores ori, lurji da wiTeli kamaTeli. ipoveT imis albaToba, rom lurj kamaTelsa da wiTel kamaTelze mosuli ricxvebis sxvaoba toli iqneba –2-is, 1-is. SeadgineT p Sesabamisobis cxrili, sadac p: mosul ricxvTa sxvaoba → am sxvaobis mosvlis albaToba (igulisxmeba lurj kamaTelze mosul ricxvs gamoklebuli wiTel kamaTelze mosuli ricxvi). aageT p Sesabamisobis grafiki. iqneba Tu ara es Sesabamisoba funqcia? cxrili 1 0 1 2 3 4 5 –1 0 1 2 3 4 –2 –1 0 1 2 3 –3 –2 –1 0 1 2 –4 –3 –2 –1 0 1 –5 –4 –3 –2 –1 0 1-li cxrilis saSualebiT SevadginoT p Sesabamisobis cxrili. sxvaoba –5 –4 –3 –2 –1 0 1 2 3 4 5 albaToba 1 36 2 36 3 36 6 – |m| 6 – |m| p : m → , anu p(m) = , m ∈ {–5; –4; –3; ...; 4; 5} 36 36 p(–2) = 4 1 5 36 = 9 ; p(1) = 36 . p Sesabamisoba funqciaa. avagoT am funqciis grafiki. 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 36
funqciis mniSvnelobaTa simravlea E(p) = { 1 ; 2 ; 3 ; 4 ; 5 ; 6 36 36 36 36 36 36} miRebuli grafikidan kidev sxva Tvisebebis amokiTxvac SegviZlia. rogor icvleba mosuli ricxvebis sxvaobis albaToba, roca m izrdeba: a) –5-dan 0-mde? b) 0-dan 5-mde? rogoria m-is da –m-is mosvlis albaToba? aqvs Tu ara p funqcias simetriis RerZi? simetriis centri? CamoayalibeT areze mocemuli winadadebis sawinaaRmdego winadadeba. SeavseT gamotovebuli adgilebi: 1. X da Y simravleebs Soris Sesabamisobas, roca X simravlis nebismier elements Seesabameba Y simravlis ? funqcia ewodeba. 2. a elements b elementis ? ewodeba, b elements ki a elementis ? . 3. CasviT gamotovebul adgilas niSnebi ; = naxazze mocemuli y=f(x) funqciisTvis: f(–3) ? 0; f(2) ? 0; f(3) ? f(–1); f(–1) ? 0. b 4. f funqciisTvis D(f) = ? ; E(f) = ? . 5. marTkuTxa sakoordinato sibrtyis yvela im wertilTa simravles, romelTa koordinatebi akmayofilebs y=f(x) gantolebas, y=f(x) funqciis ? ewodeba. 6. mocemuli y=x 2 –1 funqciisTvis, roca argumentis mniSvneloba udris 3-s, maSin funqciis mniSvneloba tolia ? , xolo roca funqciismniSvnelobaa3-istoli,maSinargumentismniSvneloba udris ? . yuradReba! y 2 x y 1 2 y2 f wiri ar aris funqcia f – funqciaa sakoordinato sibrtyeSi mocemuli wiri aris funqcia, Tu y RerZis paraleluri nebismieri wrfe wirs kveTs araumetes erT wertilSi. 11
Page 3: nana jafariZe maia wilosani nani
Page 6 and 7: IV Tavi . . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 f funqciaa h ar aris funqc
Page 14 and 15: I Tavi -4 12 4 a) savarjiSoebi: 1 r
Page 16 and 17: I Tavi 14 4) rodis moawyves turiste
Page 18 and 19: I Tavi 16 2 amovicnoT wrfivi funqci
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 22 and 23: I Tavi 20 proeqti: gazomvebidan fun
Page 24 and 25: I Tavi 22 y 10 -3 -2 -1 0 1 2 3 9 8
Page 26 and 27: I Tavi 24 15% 1,5 < n ≤ 2 20% 1 <
Page 28 and 29: I Tavi 26 nax. 1 kvadratul gantoleb
Page 30 and 31: I Tavi 28 3 dawereT kvadratuli gant
Page 32 and 33: I Tavi davazustoT! roca D = 0, kvad
Page 34 and 35: I Tavi 32 amovxsnaT formuliT (3x 2
Page 36 and 37: I Tavi 34 z) 10x 2 −120 + 6x = 98
Page 38 and 39: I Tavi navis sakuTari siCqarea navi
Page 40 and 41: I Tavi 38 6 amovxsnaT jgufuri mecad
Page 42 and 43: I Tavi x 1 da x 2 ricxvebi arian x
Page 44 and 45: I Tavi 42 17 amoxseniT gantoleba: a
Page 46 and 47: I Tavi 44 yuradReba: Tu D=0, maSin,
Page 48 and 49: I Tavi gavixsenoT! x = a, maSin a 2
Page 50 and 51: I Tavi 48 I Tavis damatebiTi savarj
Page 52 and 53: I Tavi 50 K y = x 2 A B -3 -2 -1 K
Page 54 and 55: I Tavi 52 39 A punqtidan B punqtisa
Page 56 and 57: I Tavi narevSi gaxsnili nivTierebis
Page 58: 56 I TavSi Seswavlili masalis mokle

I Tavi

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