How do you graph #y=sqrtx-3#, compare it to the parent graph and what is the domain and range?

1 Answer
Aug 27, 2017

Standard graph of #y=sqrtx# transformed (shifted) 3 units negative (down) on the #y-#axis.
Domain; [0, +oo); Range: [-3, +oo)

Explanation:

#y = sqrtx-3#

Graphically, #y# is the standard graph of #y = sqrtx# transformed (shifted) 3 units negative (down) on the #y-#axis. As can be seen by the graph of #y# beow.

graph{sqrtx-3 [-1.28, 16.5, -4.204, 4.686]}

#y in RR# is defined where #x>=0#

Hence, the domain of #y# is #[0, +oo)#

Then, #y_min = y(0) = -3#

Since #y# has no upper bound, the range of #y# is [-3, +oo)