Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises: 6


Applying vertical stretching by factor of $2$ and then the translation by $2$ to the right we get $$y=2\sqrt{7x-10-x^2}.$$

Work Step by Step

Fist note that the "width" of the graph remains the same because $3-0=5-2$. This means that there is no horizontal stretching/shrinking, only rightwards translation by $2$. Then note that the maximum of the original function is at $1.5$ while for the new function it is $3$ which is $2$ times bigger so there is vertical stretching by the factor of $2$. Applying these transformations: $$f(x)\to f(x-2)\to 2f(x-2)$$ so the function from the graph is actually $$y = 2\sqrt{3(x-2)-(x-2)^2} =\\2\sqrt{3x-6-x^2+4x-4}=2\sqrt{7x-10-x^2}.$$
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