Left and right ends of the given poynomial function will fall downwards (towards negative infinity).
End behavior of a polynomial:
- If a polynomial function is f(x) = ax⁴ + bx³ + cx² + dx + e
Leading coefficient → a
Degree of the polynomial = 4
- If the degree is even and leading coefficient is negative (-), left end and right ends fall downwards.
Given in the question,
Poynomial function → g(x) = -x⁴ + 2x³ + 5x² - 1
Degree of the polynomial = 4 (even)
Leading coefficient = -1 (negative)
Therefore, left end of the graph will fall downwards (towards negative infinity) and the right end of the graph will fall downward (towards negative infinity).
Learn more about the end behaviour of a polynomial here,
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