Answer
(a) $III$
(b) $I$
(c) $IV$
(d) $II$
Work Step by Step
(a) As we can see in the $x =f(t)$ graph, $x$ can only have values greater than $1$. The only parametric curve that follows that rule is $III$.
(b) According to the $x = f(t)$ and the $y = f(t)$ graph, the curve passes through $x=2$ exactly two times, and through $y = 2$ three times. The only parametric curve that does that is $I$
(c) According to the $x = f(t)$ and the $y = f(t)$ graph, the curve passes through $x=2$ exactly two times, and $y$ does not have negative values. The only parametric curve that follows these rules is $IV$
(d) According to the $x = f(t)$ and the $y = f(t)$ graph, the x value is temporarily constant at $x=2$. The only parametric curve that does that is $II$
