Mienzaniso yeMibvunzo Inokurukura nezveDomain, Codomain, uye Range
Kunzwisisa pfungwa dzenzvimbo, nzvimbo, uye nzvimbo mu masvomhu, kunyanya mabasa, kwakakosha kune chero mudzidzi ari kudzidza ndima iyi. Pfungwa idzi dzakakosha kumapazi akasiyana-siyana emasvomhu, kusanganisira masvomhu chaiwo, nhamba, uye sainzi yemakombiyuta. Chinyorwa chino chichakurukura mienzaniso yezvinetso zvine chekuita nenzvimbo, nzvimbo, uye nzvimbo, netsananguro dzakakwana.
Pfungwa Dzekutanga
Domain
Domain ndiyo seti yezvose zvinopinzwa (x) zvinogona kugamuchirwa nebasa. Muchidimbu, domain ndiyo zvese zvinogoneka zvatinogona kuisa mubasa racho.
Nzvimbo yeCodomain
Codomain ndiyo seti yezvose zvinogoneka, asi zvisingadiwi hazvo, zvinobuda zvinogadzirwa nebasa. Codomain inogona kusiyana nerenji, asi inofanira kunge yakafukidza renji yacho.
dungwerungwe
Range ndiyo seti yezvose zvinobuda (y) zvinogadzirwa nebasa rezvose zvinopinda mudomain.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1
Zvichienderana nebasa f(x) = 2x + 3. Sarudza domain, codomain, uye range yebasa kana domain iri nhamba chaidzo.
Kukurukurirana:
– Domain: Zvichienderana nekuti domain yese inhamba chaiyo, saka \( \text{Domain} = \mathbb{R} \).
– Codomain: Codomain yebasa inogona kufungidzirwawo kuti inhamba chaiyo, kureva \( \text{Codomain} = \mathbb{R} \).
– Range: Kuti tiwane range, tinofanira kunzwisisa mashandiro anoita basa racho. Basa \( f(x) = 2x + 3 \) ibasa rakatsetseka rinofukidza range rese remanhamba chaiwo, nekuti pamutengo wega wega we \( x \in \mathbb{R} \), \( f(x) \) inhamba chaiyo zvakare uye inofukidza mavalues ese ari mu \(\mathbb{R}\). Saka, \( \text{Range} = \mathbb{R} \).
Mubvunzo 2
Zvichienderana nebasa rekuti g(x) = sqrt(x – 1). Sarudza nzvimbo, nzvimbo, uye huwandu hwebasa racho.
Kukurukurirana:
– Domain: Basa rekuti g(x) rinosanganisira midzi midiki, iyo inoshanda chete kune vasiri negative values pasi pe radical. Saka, kune \( x – 1 \geq 0 \), ipapo \( x \geq 1 \). Saka, \( \text{Domain} = [1, \infty) \).
– Codomain: Kazhinji tinofunga kuti codomain yebasa iri inhamba chaiyo isiri negative nekuti square root inogara isiri negative. Saka, \(\text{Codomain} = [0, \infty)\).
– Range: Kune range, tinotarisa ma values chaiwo anodzoserwa nebasa racho. Kana \( x \geq 1 \), ipapo \( g(x) = \sqrt{x – 1} \geq 0 \). Hazvina mhosva kuti \( x \ yakakura sei), mhedzisiro ye \( \sqrt{x – 1} \) ichagara iri mu range \([0, \infty)\). Saka, \(\text{Range} = [0, \infty)\).
Mubvunzo 3
Zvichienderana nebasa rekuti h(x) = 1/x. Sarudza nzvimbo, nzvimbo, uye huwandu hwebasa iri.
Kukurukurirana:
– Domain: Basa \( h(x) = \frac{1}{x} \) harina kutsanangurwa kana \( x = 0 \) nekuti rinozoguma nekukamurwa ne zero. Saka \( \text{Domain} = \mathbb{R} – \{0\} \) kana \( \text{Domain} = (-\infty, 0) \cup (0, \infty) \).
– Codomain: Tinogona kufunga kuti codomain inhamba dzese chaidzo, kunyangwe kana kukosha \( x = 0 \) kusina kubva kudomain, codomain inogona kuramba iri \( \mathbb{R} \).
– Range: Parange, tinotarisa mhedzisiro ye \( h(x) \) pamusoro pemakoshero ese e \( x \) mudomeni. Kukosha kwe \( 1/x \) hakumbofi kuri 0, asi kunogona kusanganisira nhamba dzese dzechokwadi dzisina kunaka nedzakanaka kunze kwe zero pachayo. Saka \(\text{Range} = \mathbb{R} – \{0\}\).
Mubvunzo 4
Zvichienderana nebasa k(x) = x^2 – 4. Sarudza nzvimbo, nzvimbo, uye huwandu hwebasa racho.
Kukurukurirana:
– Domain: Sezvo basa \( k(x) \) riri polynomial yedhigirii rechipiri, domain yaro yese inhamba chaidzo, \( \text{Domain} = \mathbb{R} \).
– Codomain: Kune mabasa epolynomial, tinogona kufunga kuti codomain inhamba chaidzo, \( \text{Codomain} = \mathbb{R} \).
– Range: Basa re quadratic rinogona kuongororwa kubva pa parabola \( y = x^2 – 4 \). Parabola iyi inovhura kumusoro nepoindi shoma pa \( y = -4 \). Saka, kukosha kushoma kwebasa iri i -4, uye mushure meizvozvo inogona kusvika chero kukosha kwakakura kupfuura -4. Saka, \(\text{Range} = [-4, \infty) \).
Aya ndiwo mimwe mienzaniso yezvinetso nehurukuro dzine chekuita nedomain, codomain, uye range. Kunzwisisa pfungwa idzi nhatu hakungobatsiri kugadzirisa matambudziko chete asiwo kunopa ruzivo rwakadzama rwekuti basa rinoita sei mumamiriro ezvinhu akakura emasvomhu. Nekudzidzira nguva dzose, kunzwisisa kwako domain, codomain, uye range kuchasimba uye kuchasimba.
