Write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.

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.