10. The graph of $y=f(x)=b^{x}$, where $b>1$, is translated such that the equation of the new graph is expressed as $y-2=f(x-1)$. The range of the new function is

Step 1 ：First, let's understand the meaning of the problem. We are given a function $y=f(x)=b^x$, where $b>1$, and we need to find the range of the new function after translation: $y-2=f(x-1)$.

Step 2 ：Now, let's rewrite the new function in terms of $f(x)$: $y=f(x-1)+2$.

Step 3 ：Since the original function $f(x)=b^x$ is an exponential function with a base greater than 1, its range is $(0,\infty)$.

Step 4 ：The new function is a translation of the original function by 1 unit to the right and 2 units up. This means that the range of the new function will also be shifted 2 units up.

Step 5 ：So, the range of the new function is $(0+2,\infty)=(2,\infty)$.

Step 6 ：\(\boxed{(2,\infty)}\) is the final answer.