Imibuzo Yesibonelo Exoxa Ngokuhlanganisa Ukuguqulwa Komsebenzi
Ukuguqulwa komsebenzi kuyisihloko esibalulekile kwizibalo, ikakhulukazi ekufundweni kwemisebenzi namagrafu ayo. Ukusetshenziswa kokuguqulwa komsebenzi kuhilela imisebenzi ehlukahlukene njengokuhumusha, ukuzindla, ukunwebeka, kanye nokujikeleza. Kulesi sihloko, sizohlola ukuthi yikuphi ukuguqulwa komsebenzi okuhlanganisiwe nokuthi singakuxazulula kanjani ngezinkinga eziningana zezibonelo.
Iyini inhlanganisela yokuguqulwa komsebenzi?
Ukuguqulwa komsebenzi kuhilela ukushintsha isikhundla noma ukuma kwegrafu yomsebenzi wokuqala. Ukuhlanganiswa kokuguqulwa komsebenzi kusho ukuhlanganisa ukuguqulwa okubili noma ngaphezulu komsebenzi owodwa.
Ezinye izinhlobo ezivamile zokuguqulwa komsebenzi yilezi:
– Ukuhumusha (Shift):
– Okuvundlile: \( f(x) \kuya ku-f(x – h) \) shintshela kwesokudla ngo-\( h \)
– Okuqondile: \( f(x) \kuya ku-f(x) + k \) shintsha ibanga \( k \)
- Ukuzindla:
– Okuvundlile (ngokuphathelene ne-y-axis): \( f(x) \kuya ku-f(-x) \)
– Okuqondile (ngokuqondene ne-x-axis): \( f(x) \kuya -f(x) \)
– Ukwanda (Ukwenyuka):
– Okuvundlile: \( f(x) \kuya ku-f(ax) \) kanye \( a \) njengesici sesikali esivundlile
– Okuqondile: \( f(x) \kuya ku-kf(x) \) kanye \( k \) njengesici sesikali esiqondile
Imibuzo Eyisibonelo Nengxoxo
Umbuzo 1:
Uma ubheka umsebenzi wokuqala \( f(x) = x^2 \). Thola uhlobo olusha lomsebenzi ngemva kokusetshenziswa kwenhlanganisela elandelayo yokuguqulwa:
1. Ukuhumusha okuvundlile ngakwesokudla ngamayunithi amathathu.
2. Ukwanda okuqondile okunesilinganiso esingu-2.
Ingxoxo:
1. Ukuhumusha Okuvundlile:
Umsebenzi \( f(x) = x^2 \) uma ushintshelwa kwesokudla ngamayunithi ama-3 uba \( f(x – 3) = (x – 3)^2 \).
Ngakho-ke umsebenzi omusha ngemuva kokuhumusha okuvundlile ngu-\( f_1(x) = (x – 3)^2 \).
2. Ukwanda Okuqondile:
Ngemva kokwandiswa okuqondile ngesilinganiso esingu-2, ifomu liba \( 2 \times f_1(x) = 2(x-3)^2 \).
Umphumela wokugcina womsebenzi ngemuva kokuhlanganiswa kokuguqulwa ngu:
\[ g(x) = 2(x – 3)^2 \]
Umbuzo 2:
Uma unikezwe umsebenzi \( f(x) = \sqrt{x} \). Thola uhlobo olusha lomsebenzi ngemva kokunikezwa kwenhlanganisela elandelayo yokuguqulwa:
1. Ukuzindla nge-y-axis.
2. Ukuhumusha okuqondile kuya phansi ngamayunithi amabili.
Ingxoxo:
1. Ukuzindla nge-y-axis:
Umsebenzi \( f(x) = \sqrt{x} \) ubonakala nge-y-axis, ngakho uba \( f(-x) = \sqrt{-x} \).
2. Ukuhumusha Okuqondile:
Umsebenzi wokubonakalisa ophumayo ube usushintshwa phansi ngamayunithi ama-2 ukuze ube \( \sqrt{-x} – 2 \).
Ngakho-ke, ifomu lokugcina lomsebenzi ngemuva kokuguqulwa yileli:
\[ g(x) = \sqrt{-x} – 2 \]
Umbuzo 3:
Uma unikezwe umsebenzi \( f(x) = \frac{1}{x} \). Thola uhlobo olusha lomsebenzi ngemva kokusebenzisa inhlanganisela elandelayo yokuguqulwa:
1. Ukuhumusha okuvundlile ngakwesobunxele ngamayunithi angu-4.
2. Ukwanda okuvundlile ngesici sesikali \(\frac{1}{2}\).
Ingxoxo:
1. Ukuhumusha Okuvundlile:
Umsebenzi \( f(x) = \frac{1}{x} \) ngemva kokushintshwa uye kwesobunxele ngamayunithi angu-4 uba \( f(x + 4) = \frac{1}{x + 4} \).
2. Ukwanda Okuvundlile:
Umsebenzi wokuhumusha ophumayo ube usunwetshwa ngokuvundlile yi-factor \(\frac{1}{2}\) ukuze ube \( f\left( \frac{x}{\frac{1}{2}} + 4 \right) = f(2x + 4) = \frac{1}{2x + 4} \).
Ngakho-ke ifomu lokugcina lomsebenzi ngemuva kokuguqulwa yileli:
\[ g(x) = \frac{1}{2x + 4} \]
Umbuzo 4:
Uma unikezwe umsebenzi \( f(x) = \sin x \). Thola uhlobo olusha lomsebenzi ngemva kokunikezwa kwenhlanganisela elandelayo yokuguqulwa:
1. Ukwanda okuqondile okunesilinganiso esingu-3.
2. Ukuzindla nge-x-axis.
Ingxoxo:
1. Ukwanda Okuqondile:
Umsebenzi wokuqala \( f(x) = \sin x \) ngemva kokwanda okuqondile okunesilinganiso esingu-3 uba \( 3 \sin x \).
2. Ukuzindla nge-x-axis:
Umsebenzi wokukhulisa ophumelayo ube usubonakala mayelana ne-x-axis, ukuze ube \( -3 \sin x \).
Umphumela wokugcina womsebenzi ngemuva kokuhlanganiswa kokuguqulwa ngu:
\[ g(x) = -3 \sin x \]
Isicelo ku-Graphics
Ukuqonda inhlanganisela yokuguqulwa komsebenzi nakho kubaluleke kakhulu ekutadisheni amagrafu aleyo misebenzi. Nazi ezinye izinto ezibalulekile okufanele uzikhumbule:
1. Uchungechunge Lokuguqulwa:
Indlela okwenziwa ngayo izinguquko ivame ukuthinta umphumela wokugcina. Isibonelo, uma senza ukunwetshwa ngaphambi kokuhumusha, umphumela wokugcina uzohluka kunokuba ngabe uhlelo lokuguqulwa luhlehlisiwe.
2. Umfanekiso ocacile:
Ukuguqulwa ngakunye kuthinta ukuma kwegrafu ngendlela ethile:
– Ukuhumusha kushintsha igrafu ngaphandle kokushintsha isimo sayo.
– Ukwanda kushintsha “ububanzi” noma “ukulahleka” kwegrafu.
– Ukuzindla kukhombisa igrafu ezungeze umugqa.
3. Ukuzijwayeza Okuqhubekayo:
Imisebenzi yokuhlela igrafu esekelwe ekuguqulweni kuyindlela ephumelelayo yokuqonda lo mqondo. Ungazama ukuhlela imisebenzi enikezwe emibuzweni yengxoxo engenhla ukuze ubone ukuthi amagrafu abo ashintsha kanjani.
Isiphetho
Ukuguqulwa komsebenzi kuwumqondo oyisisekelo kwizibalo osetshenziswa emikhakheni eyahlukene, kokubili kwezemfundo kanye nokusebenzayo. Ukufunda inhlanganisela yokuguqulwa komsebenzi kudinga ukuqonda izisekelo zohlobo ngalunye lokuguqulwa. Ngokuzijwayeza kanye nezibonelo, singaba yingcweti emisebenzini yokudweba kanye neyokudweba. Ukuzijwayeza okuqhubekayo kuzokwenza ube nekhono lokuqonda ukuthi imisebenzi ishintsha kanjani ngokuguqulwa okuhlukahlukene.
