End Behavior of Polynomials

End Behavior of Polynomials

Read each question carefully and determine the end behavior of the given polynomial functions. Indicate whether the graph rises or falls to the left and to the right.

1. What is the end behavior of the polynomial function f(x) = 3x^4 - 2x^2 + 5?

2. For the polynomial g(x) = -x^3 + 4x^2 - x + 1, describe its end behavior.

3. If a polynomial has an even degree and a positive leading coefficient, its graph will   to the left and   to the right.

4. The end behavior of a polynomial function is determined by its   and  .

5. For the function h(x) = -2x^6 + 7x^5 - 3x + 10, as x approaches positive infinity, h(x) approaches  .

6. A polynomial with an odd degree and a negative leading coefficient will have its graph fall to the left and rise to the right.

7. The end behavior of f(x) = x(x-1)(x+2) is the same as the end behavior of f(x) = x^3.

8. Describe the end behavior of the polynomial function p(x) = -5x^4 + 2x^3 - 8x + 1.

9. A polynomial function's graph rises to the left and falls to the right. What can you conclude about its degree and leading coefficient?

10. Consider the graph of a polynomial function below. Based on its end behavior, what can you infer about the degree and leading coefficient of the polynomial?