Answer
$kx^{−3}$ is $f(x)$.
$f(x) = 10x−3$
$kx^2$ is $g(x)$
$g(x) = \frac{x^{2}}{2}$
$kx^\frac{3}{2}$ is $h(x)$
$h(x) = 2x^{1.5}$
Work Step by Step
In all cases k must be positive, or negative values would appear in the chart. Only $kx^{−3}$ decreases, so that must be $f(x)$. Next, $kx^2$ grows faster than $kx^\frac{3}{2}$, so that would be $g(x)$, which grows faster than $h(x)$ (to see this, consider ratios of successive values of the functions). Finally, experimentation for values of k yields (approximately) $f(x) = 10x−3, g(x) = \frac{x^{2}}{2}, h(x) = 2x^{1.5}$
