Chapter 5 - Section 5.1 - Introduction to Polynomials and Polynomial Functions - Exercise Set - Page 326: 79

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As $x$ increases or decreases without bound, the graph of a polynomial function eventually rises or falls. In particular, 1. for odd-degree polynomials if the leading coefficient is positive, the graph falls to the left and rises to the right. If the leading coefficient is negative, the graph rises to the left falls to the right. 2. for even degree polynomials if the leading coefficient is positive, the graph rises to the left and right. If the leading coefficient is negative, the graph falls to the left and right. Thus, first check leading degree of the polynomial and then check leading coefficient to determine according to above.