Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 171: 7



Work Step by Step

The function is $y=-\tan x$. In the general equation $y=a\tan bx$, when $a\lt0$, the graph is reflected across the x-axis. In addition, comparing $y=-\tan x$ to $y=a\tan bx$, we find that $b=1$. The value of $b$ can be used to find the location of the two vertical asymptotes: $bx=-\frac{\pi}{2}$ and $bx=\frac{\pi}{2}$ $1x=-\frac{\pi}{2}$ and $1x=\frac{\pi}{2}$ $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$ The location of the asymptotes is the same as that of the graph of $\tan x$. Therefore, using this information, we can ascertain that the graph of $y=-\tan x$ will be the same as the graph of $y=-\tan x$ except that it will be reflected across the x-axis. This means that the correct graph for $y=-\tan x$ is C.
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