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 - Page 258: 36

Answer

$a.\quad -12 $ and $-3.$ $b.\quad -5 $ and $4.$ $c.\quad -8 $ and $1.$ $d.\quad -1 $ and $8.$

Work Step by Step

$(-8,0)$ and $(1,0)$ are points on the graph of y=f(x). $a.$ The graph of f(x) is translated to the left by $4$ units, so the new intercept points are $(-8-4,0)$ and $(1-4,0)$ x-intercepts: $-12 $ and $-3.$ $b.$ The graph of f(x) is translated to the right by $3$ units, so the new intercept points are $(-8+3,0)$ and $(1+3,0)$ x-intercepts: $-5 $ and $4.$ $c.$ The graph of f(x) is vertically stretched, so the new intercept points are $(-8,0\cdot 2)$ and $(1,0\cdot 2)$ x-intercepts: $-8 $ and $1.$ $d.$ The graph of f(x) is reflected about the y-axis, so the new intercept points are $(-(-8),0)$ and $(-1,0)$ x-intercepts: $-1 $ and $8.$
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