Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.1 - Exponential Functions - Exercise Set - Page 448: 28

Answer

domain: $(-\infty,\infty)$ range: $(2,\infty)$ asymptote: $ y=2$

Work Step by Step

The graph of $ f(x)=2^{x}$ is - always above the x-axis, - the x-axis ( $ y=0$ ) is the asymptote. - from left to right, always rises and passes through $(-1,\displaystyle \frac{1}{2}),\ (0,1)$, $(1,2)$, and $(2,4)$. Plot these points and join with smooth curve (black, dashed line). $ g(x)=2^{x}+2=f(x)+2$, so its graph is obtained by shifting the graph of $ f(x)$ up by 2 units. (the asymptote moves up to $ y=2$ ) Perform the transformation on the four points found above, and join the new points with a smooth curve (red, solid line). domain: $(-\infty,\infty)$ range: $(2,\infty)$ asymptote: $ y=2$
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