Let the domain of f(x) be [-1,3] and the range be [0,4]. find the domain and range of f(x−1).

We have here a genuine function transformation folks!

Remember these transformations:
f(x - k)  shifts the function to the right by k units
f(x + k) shifts the function to the left by k units
f(x) - k  shifts the function down by k units
f(x) + k shifts the function up by k units

PAY SPECIAL attention to the - and + and left and right, they are a little tricky!

So, we start with a function f(x) with a domain of [-1,3] (that's the horizontal area it covers) and a range of [0,4] (that's the vertical area it covers).

Transforming to f(x-1) shifts the function one unit to the right. This moves the horizontal area to the right by one unit also, so the domain is now [0,4]. The range stays the same because we did not move the function up or down, only horizontally to the right. The range of f(x-1) is still [0,4] (not to be confused with its new domain!).

f(x-1) domain is now [0,4], range stays the same as before [0,4]