#### Answer

a. rises to the left and falls to the right.
b. symmetric with respect to the origin.
c. See graph.

#### Work Step by Step

a. The leading term of the function $f(x)=-x^3+4x$ 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 rises to the left and falls to the right.
b. We test:
$f(-x)=-(-x)^3+4(-x)=x^3-4x=-f(x)$
as $f(-x)=-f(x)$, the function is symmetric with respect to the origin.
c. See graph.