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Answer on Calculus Question for hsd

Question #16953
Which of the following explains how to obtain the graph of y=2+5(1+e^(−x)) from the graph of y=e(−x)?
(a) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result up 2 units.
(b) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result down 2 units.
(c) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result up 7 units.
(d) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result down 7 units.
Expert's answer
Note that y(x) = 7 + 5e^(-x), that for every x0 y(x0) is obtained from e^(-x0) by
stretching the graph by 5 and shifting UP (+7).
Answer. c).

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