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{3x-3}-2
.$
If $x=0,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3(0)-3}-2
\\
y=\sqrt{0-3}-2
\\
y=\sqrt{-3}-2
\\
y=\text{not a real number}
\\\text{(*Note that the square root of negative numbers are imaginary numbers)}
.\end{array}
If $x=1,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3(1)-3}-2
\\
y=\sqrt{3-3}-2
\\
y=\sqrt{0}-2
\\
y=0-2
\\
y=-2
.\end{array}
If $x=\dfrac{4}{3},$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3\cdot\dfrac{4}{3}-3}-2
\\
y=\sqrt{4-3}-2
\\
y=\sqrt{1}-2
\\
y=1-2
\\
y=-1
.\end{array}
If $x=\dfrac{7}{3},$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3\cdot\dfrac{7}{3}-3}-2
\\
y=\sqrt{7-3}-2
\\
y=\sqrt{4}-2
\\
y=2-2
\\
y=0
.\end{array}
If $x=4,$ then
\begin{array}{l}\require{cancel}
y=\sqrt{3\cdot4-3}-2
\\
y=\sqrt{12-3}-2
\\
y=\sqrt{9}-2
\\
y=3-2
\\
y=1
.\end{array}
The results above are summarized in the table of values below and are used to graph the given function.
