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+6}+1
.$
If $x=-4,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(-4)+6}+1
\\
y=\sqrt{-8+6}+1
\\
y=\sqrt{-2}+1
\\
y=\text{not a real number}
\\\text{(*Note that the square root of negative numbers are imaginary numbers)}
.\end{array}
If $x=-3,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(-3)+6}+1
\\
y=\sqrt{-6+6}+1
\\
y=\sqrt{0}+1
\\
y=0+1
\\
y=1
.\end{array}
If $x=-2.5,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(-2.5)+6}+1
\\
y=\sqrt{-5+6}+1
\\
y=\sqrt{1}+1
\\
y=1+1
\\
y=2
.\end{array}
If $x=-1,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(-1)+6}+1
\\
y=\sqrt{-2+6}+1
\\
y=\sqrt{4}+1
\\
y=2+1
\\
y=3
.\end{array}
If $x=1.5,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{2(1.5)+6}+1
\\
y=\sqrt{3+6}+1
\\
y=\sqrt{9}+1
\\
y=3+1
\\
y=4
.\end{array}
The results above are summarized in the table of values below and are used to graph the given function.
