Trigonometry (10th Edition)

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

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 176: 34

Answer

No, each of these portions can not be a parabola.

Work Step by Step

No, each of these portions can not be a parabola. The equation of a parabola has this form: $y = ax^2+bx+c$ A parabola is the graph of a continuous function that only increases to $\infty$ (or $- \infty$) as $x$ goes to $\infty$ or $-\infty$. However, each portion of $y = sec~x$ or $y = csc~x$ approaches $\infty$ even though the value of $x$ is limited by an asymptote. Therefore, each of these portions of $y = sec~x$ or $y = csc~x$ can not be a parabola.
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