Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 402: 114


The function values are largely positive with increasing magnitude, as x approaches $-2$ from the left. The function values become larger without bounds, as x approaches $-2$ from the right.

Work Step by Step

According to the condition, when x approaches −2 from the left, then $f\left( x \right)$ increases without bound on the y-axis, that is, it increases up to positive infinity on the y-axis. However, it approaches negative infinity on the y-axis, when x approaches −2 from the right. By using limits, this can be shown as: $\underset{x\to -{{2}^{-}}}{\mathop{\lim }}\,f\left( x \right)=\infty $ and $\underset{x\to -{{2}^{+}}}{\mathop{\lim }}\,f\left( x \right)=-\infty $ Thus, as x approaches -2 from the left, the value of the function keeps on increasing without bounds, and when it approaches from the right, it becomes largely negative.
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