Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 5 - Linear Functions - Concept Byte - Characteristics of Absolute Value Graphs - Page 347: 2

Answer

a) Please see the graph. b) The vertex of the graph is (1,4). c) Domain: all real numbers, Range: all real numbers less than or equal to 4 d) x-intercepts: $x=-1$, $x=3$; y-intercept: $y=2$ e) If $a$ is positive, then the y-value of the vertex will be a minimum value. If $a$ is negative, then the y-value of the vertex will be a maximum value.
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Work Step by Step

a) The graph was created using graphing software. b) The vertex (in this case) is the point with the largest y value. c) All values of x make the equation valid. The maximum value of the equation, however, is 4 (since that is the vertex of the graph). d) The graph shows the equation has x-intercepts at $x=-1$ and $x=3$, and the y-intercept is at $y=2$ e) If the graph opens up, then the vertex has the minimum value for y for the graph. If the graph opens down, then the vertex has the maximum value for y for the graph.
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