Sydney is on a hiking trail that goes north to south. If Sydney hikes xx miles north, her elevation, in feet, can be found using the function f(x)=(x-1)^2+200.f(x)=(x−1) 2
+200. Negative xx values would find the elevation if Sydney hiked south. Find and interpret the given function values and determine an appropriate domain for the function.

f(-4)=f(−4)=
, means if Sydney hikes 4 miles to the
, her elevation would be
feet. This interpretation
in the context of the problem.
f(8)=f(8)=
, means if Sydney hikes 8 miles to the
, her elevation would be
feet. This interpretation
in the context of the problem.
f(4.5)=f(4.5)=
, means if Sydney hikes 4.5 miles to the
, her elevation would be
feet. This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is
.