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What is the range of a polynomial function with odd degree and even degree are they same or different

What is the range of a polynomial function with odd degree and even degree are they same or different

Grade:12

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
Dear Student,

If the degree of a polynomialf(x) is even and the leading coefficient is positive, thenf(x) → ∞ asx→ ±∞.
Iff(x) is an even degree polynomial with negative leading coefficient, thenf(x) → -∞ asx→±∞.
Iff(x) is an odd degree polynomial with positive leading coefficient, thenf(x) →-∞ asx→-∞ andf(x) →∞ asx→ ∞.
Iff(x) is an odd degree polynomial with negative leading coefficient, thenf(x) → ∞ asx→ -∞ andf(x) →-∞ asx→∞.

Thanks.

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