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: 19

Answer

The graph represents a function. (a) domain: $(0, 3)$ range: $(-\infty, 2)$ (b) x-intercept: $1$ y-intercept: none (c) The graph is not symmetric.

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 between $0$ and $3$, but not including $0$ and $3$. Thus, the domain is $(0, 3)$. The graph covers the y-values that are less than $2$. Thus, the range is $(-\infty, 2)$. (b) The graph crosses the x-axis at $(0, 1)$. Thus, the x-intercept is: $1$. The graph is asymptotic as it approaches the y-axis, so it has no y-intercept. (c) The graph is not symmetric.
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