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: 14

Answer

The graph represents a function. (a) Domain: $(-\infty, +\infty)$ Range: $(0, +\infty)$ (b) x-intercept: none y-intercept: $1$ (c) not symmetric with 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 at a maximum of one point only. Thus, the graph represents a function. (a) The graph covers the entire x-axis. Thus the domain is $(-\infty, +\infty)$. The graph only covers the region above the x-axis. Thus, the range is $(0, +\infty)$. (b) The graph has no x-intercept as it is asymptotic to the x-axis. The graph crosses the y-axis at $(0, 1)$ so the y-intercept is $1$. (c) The graph does not show symmetry to the x axis, the y axis, or the origin.
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