1. The problem is to graph polynomial functions and use the leading coefficient test to determine their end behavior. 2. The leading coefficient test states that the end behavior of a polynomial function depends on the degree and the sign of the leading coefficient. 3. For a polynomial $f(x) = a_n x^n + \dots + a_1 x + a_0$, where $a_n$ is the leading coefficient and $n$ is the degree: - If $n$ is even and $a_n > 0$, both ends of the graph go up. - If $n$ is even and $a_n < 0$, both ends go down. - If $n$ is odd and $a_n > 0$, the left end goes down and the right end goes up. - If $n$ is odd and $a_n < 0$, the left end goes up and the right end goes down. 4. To graph a specific polynomial, identify the leading term, apply the test, find intercepts and turning points, then sketch accordingly. Since no specific polynomial was given, this is the general method. Final answer: Use the leading coefficient test as described to determine end behavior before graphing any polynomial function.