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Which image best describes the end behavior of the polynomial function f(x) = −x4 +2x3−4x2+3x−5 (1 point) Responses
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GPT-4o mini
To determine the end behavior of the polynomial function \( f(x) = -x^4 + 2x^3 - 4x^2 + 3x - 5 \), we focus on the leading term, which is \(-x^4\).
1. Since the leading coefficient is negative and the degree of the polynomial is even (degree 4), we can determine the end behavior:
- As \( x \to \infty \) (x approaches positive infinity), \( f(x) \to -\infty \).
- As \( x \to -\infty \) (x approaches negative infinity), \( f(x) \to -\infty \).
Thus, the polynomial will rise towards negative infinity on both ends of the graph.
The best image to describe this end behavior would show the graph of the polynomial falling to the left and right, indicating that both ends of the graph are directed downward.
1. Since the leading coefficient is negative and the degree of the polynomial is even (degree 4), we can determine the end behavior:
- As \( x \to \infty \) (x approaches positive infinity), \( f(x) \to -\infty \).
- As \( x \to -\infty \) (x approaches negative infinity), \( f(x) \to -\infty \).
Thus, the polynomial will rise towards negative infinity on both ends of the graph.
The best image to describe this end behavior would show the graph of the polynomial falling to the left and right, indicating that both ends of the graph are directed downward.
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