Sum of Functions: Even, Odd, Neither?

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Discussion Overview

The discussion revolves around the properties of even and odd functions, specifically focusing on the behavior of their sums. Participants explore the definitions and implications of these properties, as well as personal experiences with examples.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant asks why the sum of even functions is even, the sum of odd functions is odd, and the sum of an even and an odd function is neither even nor odd.
  • Another participant suggests that the original poster should explore the definitions of even and odd functions and try adding examples to see the results.
  • A different participant mentions that they have been studying even and odd functions in school and found that their experiments with adding functions align with the generalizations they encountered online.
  • One participant advises looking up definitions of even and odd functions before asking further questions.

Areas of Agreement / Disagreement

There is no consensus on the underlying reasons for the properties of even and odd functions, and participants express varying levels of familiarity with the topic. Some participants are focused on personal exploration, while others emphasize the importance of definitions.

Contextual Notes

Participants have not fully defined what constitutes an even or odd function, and there are unresolved assumptions regarding the generalizations mentioned. The discussion does not clarify the mathematical steps involved in proving the properties of these functions.

Who May Find This Useful

This discussion may be useful for students learning about function properties, particularly those studying even and odd functions in a mathematical context.

Mishie
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Why is the sum of even functions even, the sum of odd functions odd, and the sum of an even and an odd function neither even nor odd?? Thanks in advance!
 
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This looks like homework. What do you think? What is an even/odd function? Can you try out, say, adding two even functions/ two odd functions together and see what happens? How about the case with one even and one odd? Can you generalise these?
 
No, we have been working on even/odd functions at school, so I decided to do a bit of my own research and came across a site which had the generalizations that I've mentioned. I have tried to add two even/odd functions together and found that the answers match the generalization. I am just wondering why this is and how it works (if that makes sense).
 
Then before you ask questions about "even" and "odd" functions look up the definitions!
Google "even function" and you will finds loads of things.
 

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