QuestionAugust 27, 2025

Consider the polynomial function p(x)=6x^9+4x^6+2x^4-200 What is the end behavior of the graph of p? Choose 1 answer: A Asxarrow infty ,p(x)arrow infty and as xarrow -infty ,p(x)arrow infty B Asxarrow infty ,p(x)arrow -infty and as xarrow -infty ,p(x)arrow infty C Asxarrow infty ,p(x)arrow -infty and as xarrow -infty ,p(x)arrow -infty D Asxarrow infty ,p(x)arrow infty and as xarrow -infty ,p(x)arrow -infty

Consider the polynomial function p(x)=6x^9+4x^6+2x^4-200 What is the end behavior of the graph of p? Choose 1 answer: A Asxarrow infty ,p(x)arrow infty and as xarrow -infty ,p(x)arrow infty B Asxarrow infty ,p(x)arrow -infty and as xarrow -infty ,p(x)arrow infty C Asxarrow infty ,p(x)arrow -infty and as xarrow -infty ,p(x)arrow -infty D Asxarrow infty ,p(x)arrow infty and as xarrow -infty ,p(x)arrow -infty
Consider the polynomial function p(x)=6x^9+4x^6+2x^4-200
What is the end behavior of the graph of p?
Choose 1 answer:
A Asxarrow infty ,p(x)arrow infty  and as xarrow -infty ,p(x)arrow infty 
B Asxarrow infty ,p(x)arrow -infty  and as xarrow -infty ,p(x)arrow infty 
C Asxarrow infty ,p(x)arrow -infty  and as xarrow -infty ,p(x)arrow -infty 
D Asxarrow infty ,p(x)arrow infty  and as xarrow -infty ,p(x)arrow -infty

Solution
4.0(254 votes)

Answer

D As x \rightarrow \infty, p(x) \rightarrow \infty and as x \rightarrow -\infty, p(x) \rightarrow -\infty Explanation 1. Identify the Leading Term The leading term is 6x^9. 2. Determine the Degree and Leading Coefficient The degree is 9 (odd), and the leading coefficient is 6 (positive). 3. Analyze End Behavior For an odd-degree polynomial with a positive leading coefficient, as x \rightarrow \infty, p(x) \rightarrow \infty; as x \rightarrow -\infty, p(x) \rightarrow -\infty.

Explanation

1. Identify the Leading Term<br /> The leading term is $6x^9$.<br /><br />2. Determine the Degree and Leading Coefficient<br /> The degree is 9 (odd), and the leading coefficient is 6 (positive).<br /><br />3. Analyze End Behavior<br /> For an odd-degree polynomial with a positive leading coefficient, as $x \rightarrow \infty$, $p(x) \rightarrow \infty$; as $x \rightarrow -\infty$, $p(x) \rightarrow -\infty$.
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