Answer:
[tex]y=\sqrt{x+3}-1[/tex]
Step-by-step explanation:
This is the curve of [tex]y=\sqrt{x}[/tex] with some transformations applied.
The curve appears to be moved left 3 units and down 1 unit.
The pictured curve is that of [tex]y=\sqrt{x-(-3)}-1[/tex] or after simplifying [tex]y=\sqrt{x+3}-1[/tex].
Check it!
Plug in some points on the given curve into the equation we said that fits it.
Here are some points I see on the curve:
(-3,-1)
(-2,0)
(1,1)
Let's see if those points satisfy our equation.
[tex]y=\sqrt{x+3}-1[/tex] with [tex](x,y)=(-3,-1)[/tex]:
[tex]-1=\sqrt{-3+3}-1[/tex]
[tex]-1=\sqrt{0}-1[/tex]
[tex]-1=0-1[/tex]
[tex]-1=-1[/tex] is true so (-3,-1) does satisfy [tex]y=\sqrt{x+3}-1[/tex].
[tex]y=\sqrt{x+3}-1[/tex] with [tex](x,y)=(-2,0)[/tex]:
[tex]0=\sqrt{-2+3}-1[/tex]
[tex]0=\sqrt{1}-1[/tex]
[tex]0=1-1[/tex]
[tex]0=0[/tex] is true so (-2,0) does satisfy [tex]y=\sqrt{x+3}-1[/tex].
[tex]y=\sqrt{x+3}-1[/tex] with [tex](x,y)=(1,1)[/tex]:
[tex]1=\sqrt{1+3}-1[/tex]
[tex]1=\sqrt{4}-1[/tex]
[tex]1=2-1[/tex]
[tex]1=1[/tex] is true so (1,1) does satisfy [tex]y=\sqrt{x+3}-1[/tex].
All three points that crossed nicely fit the equation we described.
