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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

2. Michele_Laino

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

and: $$a\cdot x^4$$ goes to +infinity, being $$a>0$$

4. KJ4UTS

I see that B. and C. have positive infinity

5. Michele_Laino

f(x) never goes to -infinity

6. KJ4UTS

Oh I see so that would make it choice B. then because C. goes to - infinity

7. Michele_Laino

correct! the right option is B

8. KJ4UTS

@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

if $$a<0$$ your polynomial function goes to -infinity, in both cases as x goes to +infinity or to -infinity

10. KJ4UTS

Ok thank you :)

11. Michele_Laino

:)

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