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Question 951595: I am very confused with the end behavior of a Polynomial. Someone please help me with that.
Every polynomial has one of the following behaviors:
(i) y → ∞ as x → ∞ and y → ∞ as x → −∞
(ii) y → ∞ as x → ∞ and y → −∞ as x → −∞
(iii) y → −∞ as x → ∞ and y → ∞ as x → −∞
(iv) y → −∞ as x → ∞ and y → −∞ as x → −∞
For each polynomial, choose the appropriate description of its end behavior from the list above.
(a) y = x^3 − 3x^2 + 2x − 15:
.
(b) y = −2x^4 + 19x + 100:
.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! In general, the term with the highest degree prevails, so in this case, the term you want to look at in (a) is x^3. Since x^3 --> infinity as x --> infinity, and x^3 --> -infinity as x --> -infinity, the answer to (a) is (ii).
For (b), look at the -2x^4 term.
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