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The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function. y 6 4 3 2 1 A -6 -5 -4 13 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 19 الب ·X

The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function. y 6 4 3 2 1 A -6 -5 -4 13 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 19 الب ·X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function. **Graph Explanation:** - **Axes:** - The horizontal axis (x-axis) ranges from -6 to 6. - The vertical axis (y-axis) ranges from -6 to 6. - **Line:** - A diagonal line passes through the origin (0, 0) and extends from the bottom left quadrant to the top right quadrant of the graph. - The line passes through points (-6, -6) and (6, 6). **Analysis of the Rate of Change:** - The line is straight, indicating a constant rate of change. - The slope of the line can be determined using two points on the line. From the points (-6, -6) and (6, 6): - The rise (change in y) = 6 - (-6) = 12 - The run (change in x) = 6 - (-6) = 12 - Slope (rate of change) = rise/run = 12/12 = 1 Thus, the rate of change of the function is 1.
Transcribed Image Text:The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function. **Graph Explanation:** - **Axes:** - The horizontal axis (x-axis) ranges from -6 to 6. - The vertical axis (y-axis) ranges from -6 to 6. - **Line:** - A diagonal line passes through the origin (0, 0) and extends from the bottom left quadrant to the top right quadrant of the graph. - The line passes through points (-6, -6) and (6, 6). **Analysis of the Rate of Change:** - The line is straight, indicating a constant rate of change. - The slope of the line can be determined using two points on the line. From the points (-6, -6) and (6, 6): - The rise (change in y) = 6 - (-6) = 12 - The run (change in x) = 6 - (-6) = 12 - Slope (rate of change) = rise/run = 12/12 = 1 Thus, the rate of change of the function is 1.
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