Question

if the parent function is square root x. describe the translation of of the fuction square root x-1

Answer 1

The translation of a function f(x) can be described as:
f(x)->f(x-h)+k
when the functions has been translated h units to the right, and k units up.
Compare with
sqrt(x)->sqrt(x-1)+0
we see that h=1, k=0.

Thus it is a horizontal translation of 1 unit to the right. (zero unit up).