Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mitchelsewbaran

  • 2 years ago

Give an example of an even function and explain algebraically why it is even.

  • This Question is Closed
  1. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So, an even function \(f\) is a function where for all \(x\), \(f(x) = f(-x)\). The square function and the absolute-value functions are pretty cool examples.

  2. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is that it?

  3. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Maybe.

  4. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Do you know what \(|x|\) is?

  5. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x

  6. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    And \(|-x|\).

  7. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x

  8. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Bang on!

  9. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    And do you know what \((-x)^2\) is?

  10. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x?

  11. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Nope

  12. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    o

  13. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x^2

  14. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes.

  15. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    That's correct! =)

  16. mitchelsewbaran
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so how does that answer this question, bro? :)

  17. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You just answered the question, “explain algebraically why it is even”. Look back at the definition.

  18. hba
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If f(-a)=f(a) then it is even example f(x)=x^2 f(-x)=(-x)^2 f(-x)=x^2 therfore, f(x)=f(-x) @parth explained it well :)

  19. hba
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ParthKohli *

  20. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :)

  21. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Let me do that for an absolute-value function too! So we define the absolute value function as follows\[f(x) = \cases{x \ \ \text{iff} \ \ x >0 \\ -x \ \ \text{iff} \ \ x < 0 }\]It is clear that \(f(-x)=f(x)=x\), hence an even function.

  22. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.