Question

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

Answer 1

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)