## College Algebra (6th Edition)

The Leading Coefficient Test (page 350): As $x$ increases or decreases without bound, the graph of $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+ \cdot\cdot\cdot +a_{1}x+a_{0} (a_{n}\neq 0)$ eventually rises or falls. In particular, l. For $n$ odd: If the leading coefficient is positive, the graph falls to the left and rises to the right $a_{n}>0 (\swarrow,\nearrow)$. If the leading coefficient is negative, the graph is negative, the graph rises to the left and falls to the right. $a_{n}<0 (\nwarrow,\searrow)$ 2. For $n$ even: If the leading coefficient is positive, the graph rises to the left and rises to the right. $a_{n}>0 (\nwarrow,\nearrow)$ If the leading coefficient is negative, the graph falls to the left and falls to the right. $a_{n}<0 (\swarrow, \searrow)$ ---------------------- For this function, $n$ is odd, leading coefficient is negative, we look for behavior: $(\nwarrow,\searrow)$ , to which the closest is graph (c)