Answer
a. falls to the left and also falls to the right.
b. symmetric with respect to the y-axis.
c. See graph.
Work Step by Step
a. The leading term of the function $f(x)=-x^4+25x^2$ is $-x^4$ with a coefficient of $-1$ 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 falls to the left and also falls to the right.
b. We test:
$f(-x)=-(-x)^4+25(-x)^2=-x^4+25x^2=f(x)$
Thus, the function is symmetric with respect to the y-axis.
c. See graph.
