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: 21

Answer

The graph represents a function. (a) domain: $(-\infty, +\infty)$ range: $(-\infty, 2]$ (b) x-intercepts:$-3$ and $3$ y-intercept: $2$ (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 only once. Thus, the graph represents a function. (a) The graph covers the entire x-axis. Thus, the domain is $(-\infty, +\infty)$. The graph covers the y-values below $2$. Thus, the range is $(-\infty, 2]$. (b) The graph crosses the x-axis at $(-3, 0)$ and $(3, 0)$. Thus, the x-intercepts are: $-3$ and $3$. The graph crosses the y-axis at $(0, 2)$. Thus, the y-intercept is $2$. (c) The graph is symmetric with respect to the y-axis.
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