# Chapter 5 - Exponents, Polynomials and Functions - 5-1 Polynomial Functions - Practice and Problem-Solving Exercises - Page 285: 31

The leading term has: degree: even leading coefficient: positive Therefore the end behavior of the graph is: $\underline{\text{up and up}}$

#### Work Step by Step

RECALL: The end behavior of the graph of a polynomial function is dependent on its leading term $ax^n$ and its degree $n$. (i) If the leading term's degree is even: (a) the end behavior is up and up if the leading coefficient is positive and (b) the end behavior is down and down if the leading coefficient is negative. (ii) If the leading term's degree is odd: (a) the end behavior is down and up if the leading coefficient is positive and (b) the end behavior is up and down if the leading coefficient is negative. The leading term of the given function is $9x^{10}$. The degree is even, and the coefficient is positive. Therefore the end behavior of the graph of the given function is up and up.

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