Answer
$a)$ $y=h(x)$
$b)$ $y=f(x)$
$c)$ $y=g(x)$
Work Step by Step
$a)$ $y=x^{2}$ is an even function so it is symmetrical about the y-axis. This limits the possible graphs to $g(x)$ and $h(x)$. It has a lower power than c) so it is less flat near the origin and less steep when $|x|\geq1$. Therefore it must be $y=h(x)$.
$b)$ $y=x^{5}$ is an odd function so it is symmetrical about the origin. The only graph possible is $y=f(x)$.
$c)$ $y=x^{8}$ is an even function so it is symmetrical about the y-axis. This limits the possible graphs to $g(x)$ and $h(x)$. It has a higher power than a) so it is more flat near the origin and more steep when $|x|\geq1$. Therefore it must be $y=g(x)$.
