# Chapter 10 - Radical Expressions and Equations - 10-5 Graphing Square Root Functions - Practice and Problem-Solving Exercises - Page 630: 44

see graph

#### Work Step by Step

The computations below show some of the values of $x$ and $y$ in the given equation, $y=\sqrt{x-2.5} .$ If $x=2,$ then \begin{array}{l}\require{cancel} y=\sqrt{2-2.5} \\ y=\sqrt{-0.5} \\ y=\text{not a real number} \\\text{(*Note that the square root of negative numbers are imaginary numbers)} .\end{array} If $x=2.5,$ then \begin{array}{l}\require{cancel} y=\sqrt{2.5-2.5} \\ y=\sqrt{0} \\ y=0 .\end{array} If $x=3.5,$ then \begin{array}{l}\require{cancel} y=\sqrt{3.5-2.5} \\ y=\sqrt{1} \\ y=1 .\end{array} If $x=6.5,$ then \begin{array}{l}\require{cancel} y=\sqrt{6.5-2.5} \\ y=\sqrt{4} \\ y=2 .\end{array} If $x=11.5,$ then \begin{array}{l}\require{cancel} y=\sqrt{11.5-2.5} \\ y=\sqrt{9} \\ y=3 .\end{array} Using the table of values below, the graph of the given function is shown.

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