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Consider the polynomial function

p(x)=-5x^(6)-3x^(5)+4x^(2)+6x". "
What is the end behavior of the graph of 
p ?
Choose 1 answer:
(A) As 
x rarr oo,p(x)rarr oo, and as 
x rarr-oo, 
p(x)rarr oo.
(B) As 
x rarr oo, 
p(x)rarr-oo, and as 
x rarr-oo,p(x)rarr oo.
(c) As 
x rarr oo, 
p(x)rarr-oo, and as 
x rarr-oo,p(x)rarr-oo.
(D) As 
x rarr oo,p(x)rarr oo, and as 
x rarr-oo, 
p(x)rarr-oo.

Consider the polynomial function\newlinep(x)=5x63x5+4x2+6x p(x)=-5 x^{6}-3 x^{5}+4 x^{2}+6 x \text {. } \newlineWhat is the end behavior of the graph of p p ?\newlineChoose 11 answer:\newline(A) As x,p(x) x \rightarrow \infty, p(x) \rightarrow \infty , and as x x \rightarrow-\infty , p(x) p(x) \rightarrow \infty .\newline(B) As x x \rightarrow \infty , p(x) p(x) \rightarrow-\infty , and as x,p(x) x \rightarrow-\infty, p(x) \rightarrow \infty .\newline(C) As x x \rightarrow \infty , p(x) p(x) \rightarrow-\infty , and as x,p(x) x \rightarrow-\infty, p(x) \rightarrow-\infty .\newline(D) As x,p(x) x \rightarrow \infty, p(x) \rightarrow \infty , and as x x \rightarrow-\infty , p(x) p(x) \rightarrow-\infty .

Full solution

Q. Consider the polynomial function\newlinep(x)=5x63x5+4x2+6x p(x)=-5 x^{6}-3 x^{5}+4 x^{2}+6 x \text {. } \newlineWhat is the end behavior of the graph of p p ?\newlineChoose 11 answer:\newline(A) As x,p(x) x \rightarrow \infty, p(x) \rightarrow \infty , and as x x \rightarrow-\infty , p(x) p(x) \rightarrow \infty .\newline(B) As x x \rightarrow \infty , p(x) p(x) \rightarrow-\infty , and as x,p(x) x \rightarrow-\infty, p(x) \rightarrow \infty .\newline(C) As x x \rightarrow \infty , p(x) p(x) \rightarrow-\infty , and as x,p(x) x \rightarrow-\infty, p(x) \rightarrow-\infty .\newline(D) As x,p(x) x \rightarrow \infty, p(x) \rightarrow \infty , and as x x \rightarrow-\infty , p(x) p(x) \rightarrow-\infty .
  1. Leading Term Exponent: Since the leading term has an even exponent, the end behaviors at both ends of the xx-axis will be the same.
  2. Coefficient Sign: Because the coefficient of the leading term is negative, the graph will go down on both ends.
  3. End Behavior: So, as xx approaches \infty, p(x)p(x) approaches -\infty, and as xx approaches -\infty, p(x)p(x) also approaches -\infty.

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