State the horizontal asymptote for the function $h(x)=-3^{x-1}+1$ :
$y=0$
$y=3$
$y=1$
$y=-1$

Step 1 ：The horizontal asymptote of a function is the value that the function approaches as x approaches infinity or negative infinity.

Step 2 ：For the function \(h(x)=-3^{x-1}+1\), as x approaches infinity, the term \(-3^{x-1}\) will approach negative infinity.

Step 3 ：However, as x approaches negative infinity, the term \(-3^{x-1}\) will approach 0.

Step 4 ：Therefore, the function will approach 1 from below as x approaches negative infinity.

Step 5 ：Hence, the horizontal asymptote of the function is \(y=1\).

Step 6 ：Final Answer: The horizontal asymptote for the function \(h(x)=-3^{x-1}+1\) is \(\boxed{y=1}\).