Precalculus (6th Edition) Blitzer

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

Chapter 3 - Review Exercises - Page 511: 6

Answer

Please see image for the graphs Asymptote of f: $ y=0\quad $(the x-axis) Asymptote of g: $ y=1$

Work Step by Step

The graph of $ f(x)=b^{x}$, when $ b\gt 1$, has the following characteristics: - it is above the x-axis at all times, always rising, - on the far left, it nears, but never touches the x-axis, - it rises to cross the y-axis at the point (0,1) - it rises to pass through the point (1,b), - and keeps rising... We use this information to graph $ f(x)=3^{x}.$ Calculate f(x) for several values of x, and plot the points $(x,f(x)$. Join the points with a smooth curve. Asymptote of f: $ y=0\quad $(the x-axis) --- $ g(x)=3^{x}+1=f(x)+1$ The graph of $ g $ is obtained from the graph of $ f $ by raising it upwards by 1 unit. The asymptote also rises to $ y=1.$
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