## Multivariable Calculus, 7th Edition

From the problem statement, we see that $1 \leq x \leq 4$ and $2 \leq y \leq 3$. So the curve must be contained in the range $f(t) \in [1,4]$ and $g(t) \in [2,3]$.
From the problem statement, we simply use the definition of range to find that $f(t) \in [1,4]$ and $g(t) \in [2,3]$. Note that we cannot determine anything of the domain, $(x,y)$.