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{2x}+3
.$
If $x=-1,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(-1)}+3
\\
y=\sqrt{-2}+3
\\
y=\text{not a real number}
\\\text{(*Note that the square root of negative numbers are imaginary numbers)}
.\end{array}
If $x=0,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(0)}+3
\\
y=\sqrt{0}+3
\\
y=0+3
\\
y=3
.\end{array}
If $x=0.5,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(0.5)}+3
\\
y=\sqrt{1}+3
\\
y=1+3
\\
y=4
.\end{array}
If $x=2,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(2)}+3
\\
y=\sqrt{4}+3
\\
y=2+3
\\
y=5
.\end{array}
If $x=4.5,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(4.5)}+3
\\
y=\sqrt{9}+3
\\
y=3+3
\\
y=6
.\end{array}
The results above are summarized in the table of values below and are used to graph the given function.
