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The most obvious feeling of many students entering high school is that mathematics is difficult to learn, especially the study of function, which results in students unable to reach the high level of high school mathematics. The connection of knowledge points in mathematics teaching in junior and senior high schools can help students to make a better transition and deepen their learning content. Therefore, teachers should pay special attention to the selection of teaching methods in the transition stage and improve the acceptance effect of students. This paper, starting from the connotation of core accomplishment, takes function linking teaching in junior and senior high schools as the research object, combines the current situation of function teaching in junior and senior high schools, and makes a brief discussion from the perspectives of teaching benefits, teaching effects and teaching efficiency, so as to be of benefit to the research and development of function linking teaching strategies in junior and senior high schools in China