Consider the polynomial function g(x)=−x4+2x3+5x2−1.
What is the end behavior of the graph of g ?
Choose 1 answer:
(A) As x→∞,g(x)→∞, and as x→−∞,g(x)→∞.
(B) As x→∞,g(x)→−∞, and as x→−∞,g(x)→∞.
(C) As x→∞,g(x)→−∞, and as x→−∞,g(x)→−∞.
(D) As x→∞,g(x)→∞, and as x→−∞,g(x)→−∞.
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Answer from Sia
Posted about 1 year ago
Solution by Steps
step 2
The leading term of g(x) is −x4 since it has the highest power of x
step 3
As x→∞, the leading term −x4 dominates the behavior of g(x), causing g(x)→−∞
step 4
Similarly, as x→−∞, the leading term −x4 still dominates, and since the power is even, g(x)→−∞
[question 1] Answer
C
Key Concept
End Behavior of Polynomial Functions
Explanation
The end behavior of a polynomial function is determined by its leading term. For even powers, the function approaches the same value for x→∞ and x→−∞. For negative leading coefficients, the function approaches −∞.
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