Polynomial graphed end behavior

Calculus Level 1

What is the end behavior of the graph of the following polynomial function? f ( x ) = − 4 x 5 − 8 x 3 − 3 x 2 + 7 x f(x)=-4x^5-8x^3-3x^2+7x

Falls left, rises right Rises left, falls right Falls left, falls right Rises left, rises right

Wyatt Krasnici by Wyatt Krasnici , 20, USA

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3 solutions

X X
Aug 19, 2018

It is very clear to see that lim ⁡ x → ∞ f ( x ) = − ∞ \lim_{x\to \infty}f(x)=-\infty lim ⁡ x → − ∞ f ( x ) = ∞ \lim_{x\to -\infty}f(x)=\infty So the answer is rises left,falls right

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Wyatt Krasnici
Aug 18, 2018

The correct answer is rises left, falls right.

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Hana Wehbi
Aug 19, 2018

We have the highest power is odd which is 5 5 and then the coefficient of the highest degree is negative, therefore the left tail will rise and the right tail will fall.

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