Answer
a. falls to the left and rises to the right.
b. neither.
c. see graph.
Work Step by Step
a. The leading term of the function is $x^3$, with a coefficient of $+1$ and an odd power. Thus, we can identify its end behaviors as $x\to-\infty, y\to-\infty$ and $x\to\infty, y\to\infty$. That is, the curve falls to the left and rises to the right.
b. We test:
$f(-x)=(-x)^3-(-x)^2-9(-x)+9=-x^3-x^2+9x+9$
as $f(-x)\ne f(x)$ and $f(-x)\ne -f(x)$, the function is neither symmetric with respect to the y-axis nor with the origin.
c. See graph.
