College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 388: 60

Answer

$ y=3^{\mathrm{x}} \quad$ - red graph $ y=\log_{3}x\quad$ - blue graph

Work Step by Step

$y=3^{\mathrm{x}}$ and $y=\log_{3}x$ are graphs of inverse functions. The are reflected about the line $y=x.$ $1.$ Create a table of function values. $\left[\begin{array}{llllll} x & -2 & -1 & 0 & 1 & 2\\ y=4^{x} & 1/9 & 1/3 & 1 & 3 & 9 \end{array}\right]$ Plot the points and join with a smooth curve. $2. $ Graph the line $y=x$, and then, using the (x,y) points from the table in (1), plot the points (y,x), which are their reflections across the line $y=x$. Connect the reflected points. This is the graph of $y=\log_{3}x$
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