Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 341: 14

Answer

Domain: $(-\infty, \infty)$ Range: $(4, \infty)$ Horizontal Asymptote: $y=4$

Work Step by Step

To graph the following exponential function we will first graph its base (the parent function) and apply a transformations. As we know the graph of $f(x)=e^x$ is the black dotted graph in the image. Then we can get $f(x)=e^{x−3}$ by shifting the parent function to the right by 2 units. So we will get the blue graph in the image. And finally apply last transformation $f(x)=e^{x-3}+4$ and graph it by shifting the previous graph upwards by $2$ units. Which is presented by the red graph in the image. As we have no restrictions domain of the function is $(−\infty,\infty)$. It has range of $(4,\infty)$ And a horizontal asymptote of $y=4$
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