End Behavior of Polynomials
Explore the end behavior of polynomial functions based on their degree and leading coefficient.
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End Behavior of Polynomials
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Read each question carefully and provide the best answer. Show all your work for short answer questions.
1. Which of the following describes the end behavior of the polynomial function f(x) = -3x^4 + 2x^3 - 5x + 1?
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞
As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞
As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞
2. A polynomial function has a positive leading coefficient and an odd degree. What can be said about its end behavior?
Rises to the right, falls to the left
Falls to the right, rises to the left
Rises to both the left and right
Falls to both the left and right
3. The end behavior of a polynomial function is determined by its and its .
4. If the degree of a polynomial is even and the leading coefficient is negative, then as x → ±∞, f(x) → .
5. Describe the end behavior of the function g(x) = 5x^3 - 7x^2 + 2x - 9. Justify your answer.
6. A polynomial function with an odd degree and a negative leading coefficient will have end behavior where it rises to the left and falls to the right.
True
False
7. Consider the graph of a polynomial function below. Based on its end behavior, determine if the degree is even or odd and if the leading coefficient is positive or negative.
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