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
$f(x)=2x^3+3x^2-8x-12$
is $2x^3$, with a coefficient of $+2$ 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:
$f(-x)=2(-x)^3+3(-x)^2-8(-x)-12=-2x^3+3x^2+8x-12$
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.
