## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 172: 50

#### Answer

The domain includes all real numbers except those real numbers with the following form: $x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer. The range includes all real numbers.

#### Work Step by Step

$f(x) = -4~tan(2x+\pi)$ The domain includes all real numbers, except values of $x$ such that $2x+\pi = \frac{\pi}{2}+\pi~n$, where $n$ is an integer. We can find an expression for these values of $x$: $2x+\pi = \frac{\pi}{2}+\pi~n$, where $n$ is an integer. $2x = \frac{\pi}{2}+\pi~n$, where $n$ is an integer. $x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer. The domain includes all real numbers except those real numbers with the following form: $x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer. The range includes all real numbers.

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