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KJ4UTS

  • one year ago

Which of the following best describes the end behavior of this polynomial function?

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  1. KJ4UTS
    • one year ago
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  2. Michele_Laino
    • one year ago
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    we can rewrite your polynomial function as below: \[y = {x^4}\left( {a + \frac{b}{x} + \frac{c}{{{x^2}}} + \frac{d}{{{x^3}}} + \frac{e}{{{x^4}}}} \right)\] now if x goes to +infinity or -infinity, then the sum inside the parentheses goes to a

  3. Michele_Laino
    • one year ago
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    and: \(a\cdot x^4\) goes to +infinity, being \(a>0\)

  4. KJ4UTS
    • one year ago
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    I see that B. and C. have positive infinity

  5. Michele_Laino
    • one year ago
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    f(x) never goes to -infinity

  6. KJ4UTS
    • one year ago
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    Oh I see so that would make it choice B. then because C. goes to - infinity

  7. Michele_Laino
    • one year ago
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    correct! the right option is B

  8. KJ4UTS
    • one year ago
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    @Michele_Laino Ok thank you so when a > 0 (greater sigh) it can only go to positive infinity and in a < 0 (less than) it can go to negative infinity?

  9. Michele_Laino
    • one year ago
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    if \(a<0\) your polynomial function goes to -infinity, in both cases as x goes to +infinity or to -infinity

  10. KJ4UTS
    • one year ago
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    Ok thank you :)

  11. Michele_Laino
    • one year ago
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    :)

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