College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding: 33

Answer

Option (c)

Work Step by Step

RECALL: The function $y=a \cdot f(x)$ where $a \gt 1$, involves a vertical compression by a factor of $a$ of the parent function $f(x)$. A vertical compression by a factor of$a$ means that for the same $x$ value, the value of $f(x)$ is multiplied by $a$. The given function is $y=2(fx)$. The value of $a$ is $2$. Thus, the function involves a vertical compression by a factor of $2$ of the parent function. This means that the y-value of $y=2f(x)$ is two times the y-value of $y=f(x)$. Therefore, if $(1, 3)$ is on the graph of $y=f(x)$, then the point $(1, 6)$ is on the graph of $y=2f(x)$. The answer is Option (c).
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