How do you graph #y=sqrt(x-1)# and how does it compare to the parent function?

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Answer 1 · 2018-06-20T15:36:57

Translate the parent graph by #1# to the right.

The parent function is #f(x)=sqrt(x)#, so the child function is obtained by computing #f(x-1)# instead of #f(x)#

This trasformation belong to the family of the horizontal translations, which happens everytime you change from #f(x)# to #f(x-k)#.

In particular, you translate #k# units to the left if #k>0#, or #k# units to the right if #k<0#.

In this case, #k=-1#, so this function is drawn by shifting the parent function one unit right: see below.

#f(x)=sqrt(x)#
graph{sqrt(x) [-1, 20, -1, 5]}

#f(x)=sqrt(x-1)#
graph{sqrt(x-1) [-1, 20, -1, 5]}

As you can see, the two graphs are identical, except for that #1# unit right translation.