College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.7 - Graphing Techniques - 2.7 Exercises - Page 256: 69

Answer

See the picture below
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Work Step by Step

By calculating the values of $f(x)=2\sqrt{x}+1$ (with blue) and $g(x)=\sqrt{x}$ (with red) we can see that the following equation is true for every x value: $2g(x)+1=f(x)$. In order to graph the exact parent graph, here is the table of values: $g(0)=\sqrt0=0$ $g(1)=\sqrt1=1$ $g(2)=\sqrt2=\sqrt2$ $g(3)=\sqrt3=\sqrt3$ $g(4)=\sqrt4=2$ (The square root function is not defined for negative numbers.) Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=\sqrt x$ but is wider (is stretched vertically by a factor of 2) and is translated 1 unit up.
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