Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Review Exercises: 44

Answer

$(-\infty, -2] \cup [2, +\infty)$

Work Step by Step

RECALL: The range of the function $f(x)=csc(x)$ is $(-\infty, -1] \cup [1, +\infty)$ because the value of the function will never be between in the interval $(-1, 1)$. In $f(x)=2\csc{(bx+c)}$, the value of $(bx+c)$ does not affect the range of values of the function. This means that the range of values of $f(x)=2\csc{(bx+c)}$ will never be in the interval $(-2, 2)$. Therefore, the range of a function of the form $f(x)=2\csc{(bx+c)}$ is $(-\infty, -2] \cup [2, +\infty)$.
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