# Chapter 10 - Radical Expressions and Equations - 10-5 Graphing Square Root Functions - Practice and Problem-Solving Exercises - Page 630: 51

(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.

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