## Algebra 1

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.