How do you graph #y=sqrtx-1#, compare it to the parent graph and what is the domain and range?

1 Answer
turksvids
Jan 7, 2018

domain: #x>=0#
range: #y>=-1#
same shape as parent function, just shifted down 1 unit.

Explanation:

Start with the parent function: #y=sqrt(x)#, which has domain #x>=0# and range #y>=0#.

Our new graph is of #y=sqrt(x)-1#. The #-1# represents a vertical shift of 1 unit down. It is a "rigid transformation" in that the shape of the graph remains exactly the same, you just pick up the whole thing and move it down 1 unit.

Since there is no shift left or right, the domain of #y=sqrt(x)-1# is the same as the domain of #y=sqrt(x)#, so #x>=0#. Since everything was shifted down 1 unit, the range changes from the range of the original, #y>=0#, to #y>=-1#, shifting it down 1 unit.

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