Answer
see graph
Work Step by Step
The computations below show some of the values of $x$ and $y$ in the given equation, $
y=\sqrt{x-2}+3
.$
If $x=1,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{1-2}+3
\\
y=\sqrt{-1}+3
\\
y=\text{not a real number}
\\\text{(*Note that the even root of negative numbers are imaginary numbers)}
.\end{array}
If $x=2,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2-2}+3
\\
y=\sqrt{0}+3
\\
y=0+3
\\
y=3
.\end{array}
If $x=3,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3-2}+3
\\
y=\sqrt{1}+3
\\
y=1+3
\\
y=4
.\end{array}
If $x=6,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{6-2}+3
\\
y=\sqrt{4}+3
\\
y=2+3
\\
y=5
.\end{array}
If $x=11,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{11-2}+3
\\
y=\sqrt{9}+3
\\
y=3+3
\\
y=6
.\end{array}
Using the table of values below, the graph of the given function is shown.
