Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.1 - Exponential Functions - 4.1 Exercises - Page 336: 3

Answer

First blank is $downwards$. Second blank is $right$.

Work Step by Step

To obtain the graph of $2^{x}-1$, a simple vertical translation can be applied one unit downwards so the whole function is shifted down by one unit. This is because the transformation is ''-1'' and not +1 so it is shifted downwards. On the other hand to obtain the graph of $2^{x-1}$, the graph has to be shifted to the right by one unit since this is a horizontal translation and it is to the right because of the negative sign. The negative indicates a shift to the right while a positive indicates a shift to the left.
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