A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Describe the end behavior of each function. A. y=x^4 +5 B. Y=-x^5+5x^3-2x+3

  • This Question is Closed
  1. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    HI!!

  2. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    the first one has degree 4, which is even

  3. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    also it has a positive leading coefficient (it is 1)

  4. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    therefore as \(x\to \infty\) you have \(x^4+5\to\infty\) and as \(x\to -\infty\) you have \(y^4+5\to \infty\)

  5. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    |dw:1434205740470:dw|

  6. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    do you know what a polynomial of odd degree with negative leading coefficient looks like?

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, sorry

  8. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    ok lets start with a polynomial of degree 1, a line, with negative leading coefficient, like say \(y=-x+1\) you know what that looks like?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

  10. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    it has the same "end behavior' as any polynomial of odd degree with negative leading coefficient

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok

  12. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    you got that? goes to positive infinity as x goes to negative infinity, and negative infinity as x goes to positive infinity

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So the answer is x^4+5 > infinity

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  15. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    do you know what "end behavior" means?

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Refer to the attachment

    1 Attachment
  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    both a and b are functions that have an odd number as their highest exponential degree. so the as x gets bigger, so does y. and as x gets smaller, so does y. the answer for the limit for both is |dw:1434210988972:dw| |dw:1434211163340:dw|

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just keep ∞ and ∞ in the same equation and -∞ and -∞ in the same equation. for both and you're all set

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.