College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.2 - The Graph of a Function - 3.2 Assess Your Understanding: 15


The graph represents a function. (a) domain: $[-\pi, \pi]$ range: $[-1, 1]$ (b) x-intercepts: $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ y-intercept: $1$ (c) The graph is symmetric with respect to the y-axis.

Work Step by Step

The graph passes the vertical line test since all vertical lines will pass through the graph at a maximum of one point only. Thus, the graph represents a function. (a) The graph covers the x-values from $-\pi$ to $\pi$. Thus, the domain is $(-\pi, \pi)$. The graph covers the y-values -1 to 1. Thus, the range is $[-1, 1]$. (b) The graph crosses the x-axis at $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. Thus, the x-intercepts are: $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. The graph crosses the y-axis at $(0, 1)$, so the y-intercept is $1$. (c) The graph is symmetric with respect to the y-axis
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