Respuesta :
[tex] \bf ~~~~~~~~~~~~\textit{function transformations}\\\\\\f(x)= A( Bx+ C)+ D\\\\~~~~y= A( Bx+ C)+ D\\\\f(x)= A\sqrt{ Bx+ C}+ D\\\\f(x)= A(\mathbb{R})^{ Bx+ C}+ D\\\\f(x)= A sin\left( B x+ C \right)+ D\\\\-------------------- [/tex]
[tex] \bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\~~~~~~\textit{reflection over the x-axis}\\\\\bullet \textit{ flips it sideways if } B\textit{ is negative}\\ [/tex]
[tex] \bf ~~~~~~\textit{reflection over the y-axis}\\\\\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\\bullet \textit{ vertical shift by } D\\~~~~~~if\ D\textit{ is negative, downwards}\\\\~~~~~~if\ D\textit{ is positive, upwards}\\\\\bullet \textit{ period of }\frac{2\pi }{ B} [/tex]
with that template in mind, let's check about
[tex] \bf \stackrel{parent}{y=\sqrt{x}}\qquad \qquad \qquad y=\sqrt{x}\stackrel{D}{-3} [/tex]
so √(x) -3 is really √(x) in disguise, √(x) - 3 is just √(x) with a down vertical shift of 3 units.
