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: 24

Answer

The graph represents a function. (a) domain: $(-\infty, +\infty)$. range: $(-\infty, 5]$. (b) x-intercepts: $-1$ and $2$ y-intercept: $4$ (c) The graph is not symmetric with respect to the x-axis, the y-axis, or the origin.

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 the entire x-axis. Thus, the domain is $(-\infty, +\infty)$. The graph covers the y-values below $5$. Thus, the range is $(-\infty, 5]$. (b) The graph touches the x-axis at $(-1, 0)$ and $(2, 0)$. Thus, the x-intercepts are: $-1$ and $2$. The graph crosses the y-axis at $(0, 4)$. Thus, the y-intercept is $4$. (c) The graph is not symmetric with respect to the x-axis, the y-axis, or the origin.
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