Question

How does the graph of y=sqrt(x)-3 compare to graph of y=sqrt(x)

Answer 1

`\bf ~~~~~~~~~~~~\textit{function transformations}\\\\\\f(x)= A( Bx+ C)+ D\\\\~~~~y= A( Bx+ C)+ D\\\\f(x)= A√( Bx+ C)+ D\\\\f(x)= A(\mathbb{R})^( Bx+ C)+ D\\\\f(x)= A sin\left( B x+ C \right)+ D\\\\--------------------`

`\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}\\`

`\bf ~~~~~~\textit{reflection over the y-axis}\\\\\bullet \textit{ horizontal shift by }( C)/( B)\\~~~~~~if\ ( C)/( B)\textit{ is negative, to the right}\\\\~~~~~~if\ ( 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 }(2\pi )/( B)`

with that template in mind, let's check about

`\bf \stackrel{parent}{y=√(x)}\qquad \qquad \qquad y=√(x)\stackrel{D}{-3}`

so √(x) -3 is really √(x) in disguise, √(x) - 3 is just √(x) with a down vertical shift of 3 units.