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Problem 2 Medium Difficulty
Explain how each graph is obtained from the graph of $ y = f(x) $.
(a) $ y = f(x) + 8 $
(b) $ y = f (x + 8) $
(c) $ y = 8f(x) $
(d) $ y = f(8x) $
(e) $ y = -f(x) - 1 $
(f) $ y = 8f (\frac{1}{8}x) $
Answer
a) Shift 8 units upward
b) Shift 8 units to the left
c) The function is stretched vertically by a factor of $8 .$
d) The function is shrunk horizontally by a factor of $8 .$
e) Reflect about the $x$ -axis then shift 1 unit down.
f) $y=8 f\left(\frac{1}{8} x\right)$ stretches the graph by a factor of 8 vertically and horizontally.
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Video Transcript
wow in this problem, we want to identify how each graph is obtained from the graph of fx for a through F. As the note at the top of this page indicate we're gonna rely on knowledge of transformation for the graphs. We wanted to be answer how these graphs are being the affects that relates to translations, reflections, enlargement and other transformations. So for instance in a move why people that express eight we'll be N. Y equals mx plus A. Which is known as a vertical shift. Thus we translate the graft upwards eight from fx. For being we have Y equals X plus eight. This is known as X minus a horizontal shift. So for x minus a or a is negative eight. We have shift left eight proceeding of Y equals the fx. This is an enlargement, vertical stretch being factor eight. And do we have Y equals X. This is an enlargement. So it's when we multiply the number eight inside the parentheses outside the prime T. V. As in part C. We're now doing a horizontal stretch by a factor eight. This is the different vertical and horizontal stretching and we have Y equals negative fx minus one. This is two transformation. So but first we've got to have the X axis that's for Y equals negative fx. And then similar to the question A we have a vertical shift, We're here, we're shipping one year down minus one. Finally, and F we have Y equals eight. F. 28 X. This combined their knowledge from CMD. So we have a vertical stretch factor eight and a horizontal shrink by a factor 8 to 18 graph of Y equals eight F 20 X from fx.
Harvard University
Top Calculus 3 Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Caleb E.
Baylor University
Samuel H.
University of Nottingham
