Answer
a. rises to the left and also rises to the right.
b. neither
c. see graph.
Work Step by Step
a. The leading term of the function $f(x)=3x^4-15x^3$ is $3x^4$, with a coefficient of $+3$ and an even 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 also rises to the right.
b. We test:
$f(-x)=3(-x)^4-15(-x)^3=3x^4+15x^3$
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.
