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Question 1198860: Describe the end behavior of the function f(x)=2x^7+4x^4-6.
One of the following is the correct answer. Which one is correct?
A) f(x) goes to +infinity as x goes to - infinity, and f(x) goes to +infinity as x goes to +infinity
B) f(x) goes to -infinity as x goes to - infinity, and f(x) goes to -infinity as x goes to +infinity
C) f(x) goes to -infinity as x goes to - infinity, and f(x) goes to +infinity as x goes to +infinity
D) f(x) goes to +infinity as x goes to - infinity, and f(x) goes to -infinity as x goes to +infinity
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
In any polynomial, the end behavior depends on the degree of the polynomial and the sign on the leading term. There are 4 cases:
(1) even degree, leading coefficient positive: +infinity as x goes to either +infinity or -infinity
(2) even degree, leading coefficient negative: -+infinity as x goes to either +infinity or -infinity
(3) odd degree, leading coefficient positive: +infinity as x goes to +infinity; -infinity as x goes to -infinity
(4) odd degree, leading coefficient negative: -infinity as x goes to +infinity; +infinity as x goes to -infinity
Your polynomial is odd degree with positive leading coefficient....
ANSWER: up to you
Answer by MathLover1(20850)  (Show Source):
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