Funkcija je kot matematični stroj - vstaviš število, dobiš rezultat... Show more
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Naravoslovje
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Updated May 12, 2026
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Osnovno razumevanje funkcij
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Kaj je funkcija?
Predstavljaj si funkcijo kot pametno napravo, ki deluje po jasnem pravilu. Vstaviš neko število (recimo 3), ona ga predela in ti da natančno določen rezultat. Ključno je, da za vsak vhod dobiš natanko en izhod - to je osnovno pravilo funkcij.
Te matematične stroje srečuješ povsod: pri računanju hitrosti glede na čas, pri določanju cene glede na količino blaga, ali pri spreminjanju temperature čez dan. Neodvisna spremenljivka (običajno x) je tisto, kar sam izbereš, odvisna spremenljivka (y) pa je rezultat, ki ga dobiš.
Definicijsko območje (Df) so vsi dovoljeni vhodi, zaloga vrednosti (Zf) pa vsi možni rezultati. Zapomni si: če bi en x dal dva različna y-a, to sploh ne bi bila funkcija!
💡 Nasvet: Funkcijo prepoznaš tako, da za vsak x obstaja točno en y. To je železno pravilo!
Kako predstaviš funkcijo?
Funkcijo lahko prikažeš na štiri načine, ki vsi opisujejo isto stvar. Funkcijski predpis (formula) je najpogostejši - recimo f(x) = 2x + 1. To ti pove, kaj moraš z x-om narediti, da dobiš y.
Vrednostna tabela je super, ko hočeš narisati graf. Vzameš nekaj vrednosti za x, jih vstaviš v formulo in izračunaš pripadajoče y-e. Tako za f(x) = 2x + 1 dobiš pare kot (-1, -1), (0, 1), (1, 3).
Graf je slikovni prikaz v koordinatnem sistemu - x-i gredo na vodoravno os, y-i na navpično. Vsaka točka predstavlja par (x, y). Urejeni pari so pa samo drugačen zapis tabele v oklepajih.
💡 Nasvet: Vsi štirje načini prikazujejo isto funkcijo, le da drugače. Izberi tistega, ki ti v dani situaciji najbolj ustreza!
Linearna funkcija - primer
Vzemimo funkcijo f(x) = x - 2, kjer je definicijsko območje vsa realna števila. To pomeni, da lahko za x vzameš katero koli število.
Če hočeš izračunati vrednosti, preprosto vstaviš število v formulo. Za x = 4 dobiš f(4) = 4 - 2 = 2, za x = 0 je f(0) = 0 - 2 = -2, za x = -1 pa f(-1) = -1 - 2 = -3.
V tabeli bi to izgledalo takole: (-1, -3), (0, -2), (4, 2). Če bi te točke narisal na koordinatno mrežo, bi bile vse na isti premici - zato se taki funkciji reče linearna funkcija.
💡 Nasvet: Pri linearnih funkcijah graf vedno dobi premico. Dovolj ti je izračunati samo dve točki!
Kvadratna funkcija in test funkcije
Funkcija g(x) = x² je kvadratna funkcija. Tudi tu za vsak x dobiš natanko en rezultat: g(-2) = 4, g(-1) = 1, g(0) = 0, g(1) = 1, g(2) = 4.
Opazi, da lahko različna x-a dajo isti y . To je popolnoma v redu! Pomembno je le, da en x ne da dveh različnih y-jev.
Za preverjanje, ali je graf funkcija, uporabi test z navpično premico. Če navpična črta graf seka največ enkrat, je to funkcija. Če ga seka večkrat (kot pri krožnici), to ni funkcija.
💡 Nasvet: Test z navpično premico je tvoj najboljši prijatelj za preverjanje funkcij. Deluje vedno!
Hitro ponavljanje za test
Za teste si zapomni osnove: funkcija je pravilo, ki x-u priredi točno en y. Domena (Df) so vsi možni x-i, zaloga vrednosti (Zf) pa vsi možni y-i.
Funkcijo lahko podaš s predpisom , tabelo, grafom ali urejenimi pari. Vse te načine moraš obvladati in znati pretvarjati enega v drugega.
Ne pozabi: x je neodvisna spremenljivka (ti jo izbiraš), y je odvisna (rezultat). Zapis f(x) je samo drugo ime za y, torej velja y = f(x).
💡 Nasvet: Na testu si najprej preveri, ali res velja osnovno pravilo - en x, en y. Potem lahko mirno rešuješ naprej!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Osnovno razumevanje funkcij
Funkcija je kot matematični stroj - vstaviš število, dobiš rezultat po določenem pravilu. To je eden najpomembnejših konceptov v matematiki, ki ga srečuješ povsod okrog sebe.
Kaj je funkcija?
Predstavljaj si funkcijo kot pametno napravo, ki deluje po jasnem pravilu. Vstaviš neko število (recimo 3), ona ga predela in ti da natančno določen rezultat. Ključno je, da za vsak vhod dobiš natanko en izhod - to je osnovno pravilo funkcij.
Te matematične stroje srečuješ povsod: pri računanju hitrosti glede na čas, pri določanju cene glede na količino blaga, ali pri spreminjanju temperature čez dan. Neodvisna spremenljivka (običajno x) je tisto, kar sam izbereš, odvisna spremenljivka (y) pa je rezultat, ki ga dobiš.
Definicijsko območje (Df) so vsi dovoljeni vhodi, zaloga vrednosti (Zf) pa vsi možni rezultati. Zapomni si: če bi en x dal dva različna y-a, to sploh ne bi bila funkcija!
💡 Nasvet: Funkcijo prepoznaš tako, da za vsak x obstaja točno en y. To je železno pravilo!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Kako predstaviš funkcijo?
Funkcijo lahko prikažeš na štiri načine, ki vsi opisujejo isto stvar. Funkcijski predpis (formula) je najpogostejši - recimo f(x) = 2x + 1. To ti pove, kaj moraš z x-om narediti, da dobiš y.
Vrednostna tabela je super, ko hočeš narisati graf. Vzameš nekaj vrednosti za x, jih vstaviš v formulo in izračunaš pripadajoče y-e. Tako za f(x) = 2x + 1 dobiš pare kot (-1, -1), (0, 1), (1, 3).
Graf je slikovni prikaz v koordinatnem sistemu - x-i gredo na vodoravno os, y-i na navpično. Vsaka točka predstavlja par (x, y). Urejeni pari so pa samo drugačen zapis tabele v oklepajih.
💡 Nasvet: Vsi štirje načini prikazujejo isto funkcijo, le da drugače. Izberi tistega, ki ti v dani situaciji najbolj ustreza!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Linearna funkcija - primer
Vzemimo funkcijo f(x) = x - 2, kjer je definicijsko območje vsa realna števila. To pomeni, da lahko za x vzameš katero koli število.
Če hočeš izračunati vrednosti, preprosto vstaviš število v formulo. Za x = 4 dobiš f(4) = 4 - 2 = 2, za x = 0 je f(0) = 0 - 2 = -2, za x = -1 pa f(-1) = -1 - 2 = -3.
V tabeli bi to izgledalo takole: (-1, -3), (0, -2), (4, 2). Če bi te točke narisal na koordinatno mrežo, bi bile vse na isti premici - zato se taki funkciji reče linearna funkcija.
💡 Nasvet: Pri linearnih funkcijah graf vedno dobi premico. Dovolj ti je izračunati samo dve točki!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Kvadratna funkcija in test funkcije
Funkcija g(x) = x² je kvadratna funkcija. Tudi tu za vsak x dobiš natanko en rezultat: g(-2) = 4, g(-1) = 1, g(0) = 0, g(1) = 1, g(2) = 4.
Opazi, da lahko različna x-a dajo isti y . To je popolnoma v redu! Pomembno je le, da en x ne da dveh različnih y-jev.
Za preverjanje, ali je graf funkcija, uporabi test z navpično premico. Če navpična črta graf seka največ enkrat, je to funkcija. Če ga seka večkrat (kot pri krožnici), to ni funkcija.
💡 Nasvet: Test z navpično premico je tvoj najboljši prijatelj za preverjanje funkcij. Deluje vedno!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Hitro ponavljanje za test
Za teste si zapomni osnove: funkcija je pravilo, ki x-u priredi točno en y. Domena (Df) so vsi možni x-i, zaloga vrednosti (Zf) pa vsi možni y-i.
Funkcijo lahko podaš s predpisom , tabelo, grafom ali urejenimi pari. Vse te načine moraš obvladati in znati pretvarjati enega v drugega.
Ne pozabi: x je neodvisna spremenljivka (ti jo izbiraš), y je odvisna (rezultat). Zapis f(x) je samo drugo ime za y, torej velja y = f(x).
💡 Nasvet: Na testu si najprej preveri, ali res velja osnovno pravilo - en x, en y. Potem lahko mirno rešuješ naprej!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Matematika
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Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user