What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
Answers
Given : f(x) = 3x⁶ + 30x⁵ + 75x⁴
To Find : end behavior of the graph of the polynomial function
Solution:
f(x) = 3x⁶ + 30x⁵ + 75x⁴
= 3x⁴(x² + 10x + 25)
= 3x⁴(x + 5)²
Degree is Even and leading coefficient is positive
Hence End behavior of the function
f(x) → ∞ as x → ∞
f(x) → ∞ as x → -∞
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
leading coefficient is positive Degree is Even => f(x) → ∞ as x → ∞ or x → -∞
leading coefficient is negative Degree is Even => f(x) → -∞ as x → ∞ or x → -∞
leading coefficient is positive Degree is odd => f(x) → ∞ as x → ∞
f(x → -∞ as x → -∞
leading coefficient is negative Degree is odd => f(x) → -∞ as x → ∞
f(x → ∞ as x → -∞
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