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 255: 15

Answer

See the picture below.
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Work Step by Step

The parent function is $f(x)=x^2$ (in red), but the graph of $g(x)=-\frac{1}{2}\times x^2$ (in blue) will be wider, as the coefficient multplies each y-value of the parent function by $\frac{1}{2}$ and will also be reflected across the x-axis because of the coefficient of $-1$. For drawing the exact parent graph, here is the table of values: $f(-2)= -2^2=4$ $f(-1)= -1^2=1$ $f(0)= 0^2=0$ $f(1)= 1^2=1$ $f(2)=2^2=4$ By the use of graph transformation techniques, the graph will be shrinked by a factor of $2$ and will also be reflected across the x-axis. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(-2)=-\frac{1}{2}\times -2^2=-2$ $g(-1)=-\frac{1}{2}\times -1^2=-\frac{1}{2}$ $g(0)=-\frac{1}{2}\times 0^2=0$ $g(1)=-\frac{1}{2}\times 1^2=-\frac{1}{2}$ $g(2)=-\frac{1}{2}\times2^2=-2$
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