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