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.
