Use a graphing device to graph the polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior
A) $p ( x ) \rightarrow 0$ As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $

B) $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty 3$

C) $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$

D) $p ( x ) \rightarrow - 1$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$

E) $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty$

Question

Use a graphing device to graph the polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior
A) $p ( x ) \rightarrow 0$ As $x \rightarrow \infty$ 
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $

B) $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty 3$

C) $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$

D) $p ( x ) \rightarrow - 1$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$

E) $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty$

Quizplus · Accepted Answer

The leading term of the polynomial $p(x) = -x^5 - 4x^3 - 10x$ dictates its end behavior. Since the leading term is $-x^5$, as $x$ approaches $\infty$, $p(x)$ will approach $-\infty$, and as $x$ approaches $-\infty$, $p(x)$ will approach $\infty$, due to the negative coefficient of the leading term.

Use a Graphing Device to Graph the Polynomial p(x)=−x5−4x3−10xp ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 xp(x)=−x5−4x3−10x

Use a Graphing Device to Graph the Polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$