Mienzaniso yeMibvunzo Kukurukura Mabasa neZvisiri Mabasa: Kunzwisisa Pfungwa Dzekutanga
Pengenalan
Mumasvomhu, kunyanya mu algebra, pfungwa yebasa ndeimwe yeanonyanya kukosha uye akakosha. Mabasa anotibvumira kunzwisisa hukama huripo pakati pemaseti maviri nenzira yakarongeka. Kuti tinzwisise basa, tinofanira kutanga tanzwisisa tsananguro yaro nehunhu hwaro. Nokudaro, chinyorwa chino chichaongorora matambudziko emuenzaniso uye chichakurukura mabasa neasiri mabasa. Izvi zvichatibatsira kunzwisisa zvakadzama nyaya iyi.
Tsanangudzo yeBasa uye Kusashanda
Ngatitangei nekunzwisisa tsananguro yebasa. Mumasvomhu, basa rinogona kutsanangurwa sehukama hunobatanidza chinhu chimwe nechimwe chedomain set nechinhu chimwe chete checodomain set. Nemamwe mashoko, kune chinhu chimwe nechimwe mudomain set, pane chinhu chimwe chete chinoenderana mucodomain set.
Mienzaniso yehukama huri Mabasa:
– Seti A = {1, 2, 3}
– Seti B = {4, 5, 6}
– Hukama R = {(1, 4), (2, 5), (3, 6)}
Hukama R ibasa nekuti chinhu chimwe nechimwe cheseti A chakabatanidzwa nechinhu chimwe chete cheseti B.
Chinhu chisiri basa ihukama husingasvike pazvinodiwa izvi, kureva kuti pane chinhu chimwe chete munharaunda yekutanga chakabatanidzwa nezvinhu zvinopfuura chimwe chete munharaunda yemhedzisiro.
Mienzaniso yehukama husiri Mabasa:
– Seti C = {1, 2, 3}
– Seti D = {4, 5, 6}
– Hukama S = {(1, 4), (1, 5), (2, 6)}
Hukama S hausi basa nekuti chinhu '1' muchikamu C chakabatanidzwa nezvinhu zviviri muchikamu D (zvinoti 4 ne5).
Mibvunzo yemuenzaniso nekukurukurirana
Kuti tiwedzere kunzwisisa kwedu mabasa neasiri mabasa, ngatitarisei mimwe mienzaniso yemibvunzo nehurukuro dzayo.
Muenzaniso Mubvunzo 1: Kusarudza Mabasa
Zvichipiwa seti X = {a, b, c, d} uye seti Y = {1, 2, 3, 4}, hukama hwacho hunotsanangurwa seinotevera basa here?
– R = {(a, 1), (b, 2), (c, 3), (d, 4)}
Kukurukurirana:
Ngatitarisei chinhu chimwe nechimwe mu seti X:
– 'a' inosanganiswa ne '1'
– 'b' inosanganiswa ne '2'
– 'c' yakabatana ne '3'
– 'd' yakabatana ne '4'
Sezvo chinhu chimwe nechimwe chiri mu seti X chakabatana nechinhu chimwe chete chiri mu seti Y, hukama R ibasa.
Muenzaniso Mubvunzo 2: Kuziva Mabasa kana Asiri Mabasa
Kana wapiwa seti P = {u, v, w} uye seti Q = {5, 6, 7}. Sarudza kana hukama hunotevera huri basa:
– S = {(u, 5), (v, 6), (u, 7)}
Kukurukurirana:
Ngationgororei chinhu chimwe nechimwe muchikamu P:
– 'u' yakabatana ne '5'
– 'v' yakabatana ne '6'
– 'u' inosanganisirwawo ne '7'
Sezvo chinhu 'u' muchikamu P chakabatana nezvinhu zvinopfuura chimwe muchikamu Q, hukama S hausi basa.
Muenzaniso Mubvunzo 3: Mabasa ekudhirowa kubva paGrafu
Kana wapiwa girafu yehukama pa coordinate plane, sarudza kana iri basa kana kwete. Girafu inoratidza zvinotevera:
– (1, 2)
– (2, 4)
– (3, 6)
– (4, 8)
– (5, 10)
Kukurukurirana:
Poindi yega yega iri pagirafu ine peya yefomu (x, y), izvo zvinoratidza kuti pamutengo wega wega wakapihwa we x pane mutengo mumwe chete we y wakabatana nawo. Sezvo chinhu chimwe nechimwe chiri mudunhu ichibatanidzwa nechinhu chimwe chete mudunhu, girafu yakapihwa igirafu yebasa.
Muenzaniso Dambudziko rechina: Mabasa muEquation Form
Sarudza kana equation y = x² iri basa kana domain yakapihwa iri nhamba chaidzo dzese.
Kukurukurirana:
Tinofanira kutarisa kana x-value yega yega mu domain ine y-value imwe chete yakabatana nayo. Tsiva mamwe ma x-values:
– Kana x = 1, saka y = 1² = 1
– Kana x = 2, saka y = 2² = 4
– Kana x = -1, saka y = (-1)² = 1
Zvinogona kuonekwa kuti pamutengo wega wega wakasarudzwa we x, pane mutengo mumwe chete unoenderana we y. Saka, y = x² ibasa.
Muenzaniso Mubvunzo 5: Mabasa ane Mabasa Akasiyana
Regai f(x) ive basa rinotsanangurwa na f: x → x + 3. Tsvaga zvinopesana nebasa iri, kana riripo.
Kukurukurirana:
Kana f: x → x + 3, saka tinofanira kutsvaga basa g zvekuti f(g(x)) = x uye g(f(x)) = x. Kutanga ne equation:
– y = x + 3
Kuti tiwane zvinopesana, tinoparadzanisa x:
– x = y – 3
Saka, basa re inverse ndi g(y) = y – 3.
Saka, musiyano webasa f(x) = x + 3 ndi f⁻¹(x) = x – 3.
Mhedziso
Kubva muhurukuro iri pamusoro apa, taona mienzaniso yakati wandei yematambudziko ane chekuita nemabasa nemabasa asiri ebasa, pamwe chete netsananguro dzawo. Pfungwa yebasa inotidzidzisa kuti chinhu chimwe nechimwe cheseti yedhomini chinofanira kusanganiswa nechinhu chimwe chete cheseti yedhomini. Kuziva mabasa kubva mumagirafu nemaequations inzira inobatsirawo pakuona hunhu hwehukama. Nekudzidzira marudzi aya ematambudziko, tichava neruzivo rwakawanda uye tichanzwisisa zviri nani pfungwa huru dzemabasa nemabasa asiri ebasa, ayo ari hwaro hwakakosha mualgebra nedzimwe ongororo yemasvomhu.
