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: 54

Answer

See the picture below.
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Work Step by Step

By calculating the values of $f(x)=(x−2)^2$ (with blue) and $g(x)=x^2$ (with red) we can see that for every corresponding $f(x)$ and $g(x)$ value, each x value of $g(x)$ is 2 more than the x value of $f(x)$. For drawing the exact parent graph, here is the table of values: $g(-2)= -2^2=4$ $g(-1)= -1^2=1$ $g(0)= 0^2=0$ $g(1)= 1^2=1$ $g(2)=2^2=4$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but translated 2 units right. For drawing the exact graph of $f(x)$ here is the table of values of the given function: $f(0)=(0-2)^2=4$ $f(1)=(1-2)^2=1$ $f(2)=(2-2)^2=0$ $f(3)=(3-2)^2=1$ $f(4)=(4-2)^2=4$
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