Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.5 Common Logarithms and Natural Logarithms - 12.5 Exercise Set - Page 818: 56


Domain: $\mathbb{R}$. Range: $(0,\infty)$ Graph:

Work Step by Step

The graph of this function is obtained from $f_{1}(x)=e^{x}$, by vertically stretch it by factor 2 (doubling the y-coordinates), AND by horizontally stretching it by factor 2 (doubling the the x-coordinates). AND reflecting it over the y-axis Graph, with a dashed line, the graph of $f_{1}(x)=e^{x}$, as instructed in the solution of exercise 47$:$ ...Graphing $f_{1}(x)=e^{x}$ , ... The base is $e\approx 2.718\gt 1$, so the graph rises on the whole domain. ... Asymptote is the x-axis. ... To the far left, the graph nears but does not cross the asymptote. ... The graph passes through the points ... $(-1,\displaystyle \frac{1}{e}),(0,1),(1,e),(2,e^{2})$, and so on. ... Plot these points and join with a smooth curve. Then, for each of the points used for graphing $f_{1}$ perform the above transformations (double both coordinates, reflect across y) plot the new points, and join with a smooth curve (red on the image). The asymptote remains the x-axis (double of zero is zero).
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