Answer
The possible graphs are (e), (f), (g), and (h)
Work Step by Step
If the glob is dropped, then $K=0$ at $t=0$, since the initial velocity is zero.
As the glob falls, the speed increases with time:
$v = gt$
We can write an expression for the kinetic energy at time $t$:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}m(gt)^2$
$K = \frac{1}{2}mg^2~t^2$
We can see that the kinetic energy starts at 0 and then increases as a function of $t^2$
Graph (f) is a graph for this situation.
If the glob is launched horizontally or down, then at $t=0$, $K \gt 0$ and then $K$ increases as a function of $t^2$
Graph (h) is a graph for this situation.
If the glob is launched directly up vertically, then at $t=0$, $K \gt 0$ and then $K$ decreases to zero when it reaches maximum height. After this, $K$ increases as a function of $t^2$
Graph (e) is a graph for this situation.
If the glob is launched upward with some horizontal component of motion, then at $t=0$, $K \gt 0$. Then $K$ decreases, but remains positive, until it reaches maximum height. After this, $K$ increases as a function of $t^2$
Graph (g) is a graph for this situation.
The possible graphs are (e), (f), (g), and (h).
