Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-5 Graphing Square Root Functions - Practice and Problem-Solving Exercises - Page 630: 49


(see graph)

Work Step by Step

The computations below show some of the values of $x$ and $f(x)$ in the given equation, $ f(x)=\sqrt{x+2}-4 .$ If $x=-3,$ then \begin{array}{l}\require{cancel} f(x)=\sqrt{-3+2}-4 \\ f(x)=\sqrt{-1}-4 \\ f(x)=\text{not a real number} \\\text{(*Note that the square root of negative numbers are imaginary numbers)} .\end{array} If $x=-2,$ then \begin{array}{l}\require{cancel} f(x)=\sqrt{-2+2}-4 \\ f(x)=\sqrt{0}-4 \\ f(x)=0-4 \\ f(x)=-4 .\end{array} If $x=-1,$ then \begin{array}{l}\require{cancel} f(x)=\sqrt{-1+2}-4 \\ f(x)=\sqrt{1}-4 \\ f(x)=1-4 \\ f(x)=-3 .\end{array} If $x=2,$ then \begin{array}{l}\require{cancel} f(x)=\sqrt{2+2}-4 \\ f(x)=\sqrt{4}-4 \\ f(x)=2-4 \\ f(x)=-2 .\end{array} If $x=7,$ then \begin{array}{l}\require{cancel} f(x)=\sqrt{7+2}-4 \\ f(x)=\sqrt{9}-4 \\ f(x)=3-4 \\ f(x)=-1 .\end{array} Summarizing the results above in the table of values below, the graph of the given function is shown.
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