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수학동아 - 폴리매스
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[잡담] 순전한 궁금증인데 한 번만 봐주세요
은총알 2020.05.22 07:19 조회 696

함풀문에 올리기에는 제가 답을 모를 뿐더러 답이 있는지도 모르겠어서.... 잡담에 올려봅니다.

 

자 이제 질문입니다

 

일차함수 중 y=x꼴의 일차함수를 제외하고 순서쌍 (x,y)에서 x와 y가 같은 순서쌍이 가장 많은 일차함수는 무엇일까요? 단, 여기서 x와 y는 정수입니다. x와 y가 모든 실수일 때도 궁금하네요....

  •  
    은총알 Lv.11 2020.05.22 07:21

    진짜 궁금해서 그런데 대충이라도 말해주세요!

    댓글 작성하기 좋아요0 댓글수0
  •  
    아인수타인 Lv.12 2020.05.22 07:23

    x와 y가 같은 순서쌍은 y=x와 교차하는 점이라 봐도 됩니다. 그런데 직선 2개는 (평면상에서) 일치하지 않는 이상 최대 1개 점에서 만납니다. 저기에선 일치하지 않는다고 했으므로 많아야 1개밖에 있을 수 없고, 기울기가 1인 직선 빼고 전부입니다.

    댓글 작성하기 좋아요0 댓글수8
    •  
      21세기오일러 Lv.11 2020.05.22 07:34

      +기울기가 0인직선도 빼죠

      좋아요0
    •  
      아인수타인 Lv.12 2020.05.22 07:35

      그리고 생각해보니 무한대(y축평행)도 빼야 하네요.

      좋아요0
    •  
      Turgon Lv.6 2020.05.22 07:38

      아 정정하죠 기울기가 0이고 원점을 지나는 것은 빼면 안되네요.

      마찬가지로 기울기 무한대도 원점을 지나는 것은 빼면 안되고요

      좋아요0
    •  
      아인수타인 Lv.12 2020.05.22 07:42

      그럼 일차함수가 아니잖아요.

      좋아요0
    •  
      Turgon Lv.6 2020.05.22 08:06

      네? 일차함수 아닌가요?

      좋아요0
    •  
      아인수타인 Lv.12 2020.05.22 08:14

      x축평행(기울기 0)은 상수함수, 굳이 따지자면 0차함수죠.

      좋아요0
    •  
      Turgon Lv.6 2020.05.22 08:17

      아 그렇군요

      좋아요0
    •  
      은총알 Lv.11 2020.05.22 20:07

      아 그렇군요 그럼 이차함수에서는 어떻게 되나요?

      좋아요0
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